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431 Cards in this Set
- Front
- Back
Average Acceleration
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ΔV / Δt
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Final Velocity
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Vi + at
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Displacement
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ΔX = Vi*t + 1/2(at^2)
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Final Velocity
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Vf^2 = Vi^2 + 2aΔX
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Average Velocity
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1/2 (Vi + Vf)
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Gravitational Force
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F = (G*m1*m2)/r^2
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Torque
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τ = rFsinθ
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Kinetic or Static Friction
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F(friction)≤ μ * N
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Centripital Acceleration
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(velocity)^2 / (radius)
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Centripital Force
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Mass * Acceleration
or (mass)(velocity)^2 / (radius) |
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Work
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F d cosθ
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Power
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Work/time
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Kinetic Nrg
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KE = 1/2 (mass)(velocity)^2
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Potential Nrg
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U = mass * gravity * height
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momentum
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p = mass * velocity
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Impulse
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Δp = Force * time
or m*Vf - m*Vi |
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Celsius
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C = K -273
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Thermal Expansion
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ΔL = α L ΔT
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Volume Thermal Expansion
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ΔV = β V ΔT
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Heat Gained (Q)
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Q = m c Δt
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Heat Gained (Δphase)
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Q = m * L
(L=heat of transformation constant) |
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1st Law of Thermodynamics
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ΔU = Q - W
(Q=heat nrg and W=work) |
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2nd Law of Thermodynamics
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ΔS of closed system will increase or remain unchanged
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Density
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ρ = mass / volume
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Pressure
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P = Force / Area
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Absolute Pressure
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Pabs= Patm + ρgh
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Two Pistons
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F1/A1 = F2/A2
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Boyant Force
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FB= ρ g V (where V is the volume of the object and ρ is the density of the liquid)
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Velocity in different areas of a pipe (volume flow rate)
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A1V1=A2V2
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Stress
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F/A
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Strain
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ΔL/L
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Y (Young's Modulus)
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Y= (F/A) / (ΔL/L)
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Coulomb's Law (Force b/n charges)
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F = (k*q1*q2) / r^2
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Electric Field
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E = k*q / r^2
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Force of E Field on a charge
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F = q * E
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Electric potential
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V = kq / r
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Electric Potential Nrg
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U = qV
(charge * voltage) |
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Force of B Field on charge
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q v B sinθ
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Current
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I = Δq / Δt
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Force of Wire with current
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F = I L B sinθ
(current*length*Bfield) |
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B field created by long straight wire
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B = (μo*I) / (2πr)
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B field created by loop wire
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B = (μo * I) / (2r)
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Voltage
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V = IR
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Power in circuits
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P = IV
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Resistors in series
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Rs = R1 + R2 ...
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Resistors in Parallel
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1 / Rp = 1/R1 + 1/R2 ...
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Capacitance
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C = Q / V
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E field b/n capacitor plates
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E = V / d
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Capacitors in series
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1 / Cs = 1/C1 + 1/C2 ...
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Capacitors in Parallel
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Cp = C1 + C2 ...
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Irms
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Imax / sqroot2
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Vrms
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Vmax / sqroot2
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Imax
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Irms * sqroot2
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Vmax
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Vrms * sqroot2
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Hookes Law (Force of spring)
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F = -k x
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angular freq of spring
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ω = sq root (k/m)
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angular freq of pendulum
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ω = sq root (g/L)
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Frequency
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F = 1 / T
T=period |
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Period of Spring
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T = 2π sqroot(m/k)
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Period of Pendulum
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T = 2π sqroot (L/g)
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***
Velocity of wave |
V = fλ
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Speed of Light
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c = 3x10^8
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Intensity
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I = Power / area
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Object and image formula
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1/o + 1/i = 1/f = 2/r
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Focal length
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F = radius curve / 2
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Magnification
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m = -image distance / object distance
or -i / o |
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Index of Refraction
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n = c / v
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Snell's law of refraction
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n1 sinθ1 = n2 sinθ2
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Lens Power
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P = 1 / f
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Photon Nrg
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E = h f
or E = hc/λ h= 6.6x10^-34 J*s h= 4x10^-15 eV |
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Binding Nrg
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E = Δm c^2
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Alpha Particle decay
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-4
-2 |
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-Beta decay
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+0
+1 |
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+Beta decay (positron)
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-0
-1 |
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Gamma decay
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nothing!!
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1/2 life formula
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Nf = Ni * e^(λt)
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Capacitance
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C = k*(perm. free space)* (A/d)
A=area d=distance b/n plates |
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Work done by gas expansion
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W = P*ΔV
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Vector Quantity
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Has magnitude and direction; and usually a unit of measure (The symbol is →) A vector can represent displacement, velocity, acceleration
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Scalar Quantity
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A quantity that is fully specified by giving its magnitude (mass or speed)
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Are the following scalar or vector: 1) speed; 2) weight; 3) mass; 4) velocity
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1) scalar; 2) vector; 3) scalar; 4) vector
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Newton's First Law
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A body at rest stays at rest and a body in motion stays in motion at constant velocity if no net force acts on it
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Contrast Speed vs. Velocity
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Speed has only magnitude. Velocity is a vector having magnitude and direction.
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Equation for distance at constant velocity
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see equation
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Force
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A vector quantity which is a push or pull exerted on a body.
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Newton's Second Law
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Newton's Second Law
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Uniformly Accelerated Motion
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Uniformly Accelerated Motion
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Velocity Equation for Uniform Acceleration
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Velocity Equation for Uniform Acceleration
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Acceleration Equation
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Acceleration Equation
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Equation for final velocity with uniform acceleration
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Equation for final velocity with uniform acceleration
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Equation for average speed with constant acceleration (not starting from rest)
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Equation for average speed with constant acceleration (not starting from rest)
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Describe a force in terms of its components
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A single force may be replaced by two or more forces (its component forces). These are vectors which, by using vector addition, add up to the original force.
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Torque
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The effectiveness of a force in producing rotation. Also called moment of force.
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Newton's Law of Universal Gravitation
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Two objects attract each other each other with a force that is proportionate to the product of their masses and inversely proportionate to the square of distance between them.
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Center of Gravity
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A point in or on the object where all the weight is concentrated. If supported only at this point the object will be in balance.
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Equation for average speed with constant acceleration (starting from rest
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Equation for average speed with constant acceleration (starting from rest
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Inertia
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The property by which an object resists being accelerated.
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After 6 seconds, how far will a body fall in a vacuum (g=32)
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After 6 seconds, how far will a body fall in a vacuum (g=32)
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With acceleration constant at 10 m/s2 and an initial velocity of 3 m/s, how far will a body move in 7 s?
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With acceleration constant at 10 m/s2 and an initial velocity of 3 m/s, how far will a body move in 7 s?
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With an initial velocity of 4 ft/s and a constant aceleration of 7 ft/sec2, what is the velocity after 12 s?
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With an initial velocity of 4 ft/s and a constant aceleration of 7 ft/sec2, what is the velocity after 12 s?
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Formula for final velocity given the distance s, the acceleration a, and the initial velocity Vi.
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Formula for final velocity given the distance s, the acceleration a, and the initial velocity Vi.
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Which force is referred to in Newton's second law when there is more than one force on a body
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The vector sum of all forces.
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Newton's Third Law
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When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first (action equals reaction.)
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Centripetal Force
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The inward force that must be applied to keep a body moving in a circle
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Equation for Centripetal Acceleration
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Equation for Centripetal Acceleration
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For liner motion with constant acceleration, what are the formulas for 1) distance, 2) velocity, 3) average velocity, 4) final velocity independent of time
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For liner motion with constant acceleration, what are the formulas for 1) distance, 2) velocity, 3) average velocity, 4) final velocity independent of time
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Frame of Reference
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any system for specifying the precise location of objects in space. Your frame of reference is where you view the scene from. Ex. From a moving airplane or standing in your living room
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Conservation of Momentum
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In a closed system where no external forces act, the total momentum of the system is conserved.
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Equation for Newton's Law of Gravitation
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Equation for Newton's Law of Gravitation
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Work; Equation for Work
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The product of the force on an object and the distance the object moves in the direction of the force. W = Fd; W=work in joules; F=force in Newtons; d=distance in meters
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Potential Energy; Equation for Potential Energy
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The energy stored by an object because of its position or its condition. Ex. A skier on top of a mountain has potential energy. PE = wh = mgh; w=weight; h=object height; m=mass; g=constant gravitation; PE=potential energy
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Kinetic Energy; Equation for Kinetic Energy
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Kinetic Energy; Equation for Kinetic Energy
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Equation for coefficient of sliding friction
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Equation for coefficient of sliding friction
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Equation for work against friction
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Equation for work against friction
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Power; Equation for Power
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The measure of how much work gets done per unit time; measured in watts. 1 watt = 1 joule/sec; P=W/t = Fd/t; P=power (watts); W=work (joules); t=time in seconds; F=force in newtons; d=distance in meters.
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Equation for Momentum
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P = mv; m=mass; v=velocity; P=momentum
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Line of Force
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A line drawn so that a tangent to it at any point indicates the direction of an electric or magnetic field.
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Normal Force
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A force perpendicular to the surface of an object. When you press down on the object, the normal force presses up.
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Hooke's Law
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F = -(k)x; k=spring constant; x=distortion distance; F=distortion force
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Equation for work done in stretching a spring
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Equation for work done in stretching a spring
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Equation for Change in Length when a solid expands or contracts
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Equation for Change in Length when a solid expands or contracts
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Archimedes Principle
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The apparent loss in weight of an object immersed in a fluid equals the weight of the displaced fluid.
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Bernoulli's Principle
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The greater the velocity of a fluid, the smaller its pressure.
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Equation for liquid pressure in a beaker
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P=hdg; h=height of the liquid level; d=liquid density; g=gravitational constant; P=pressure
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Two insoluble objects lose the same weight in a fluid, the objects must have the same…
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Volume. Using Archimedes Principle: the apparent loss in weight is equal to weight of the displaced fluid. They displace the same volume.
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Crest
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A region of upward displacement in a transverse wave.
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Trough
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A region of downward displacement in a transverse wave.
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Amplitude
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The maximum displacement of a vibrating particle from its equilibrium position. The height of the wave.
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Wavelength
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In a periodic wave, the distance between two adjacent troughs or two crests (λ)
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Transverse Wave
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A wave in which the vibration are at right angles to the direction of propagation of the wave. Ex, electromagnetic waves.
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Periodic Wave
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A wave repeated in each of a succession of equal time intervals.
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Longitudinal Wave
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A wave in which the vibrations are parallel to the direction of propagation of the wave. Ex. Sound waves.
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Hertz
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The frequency of sound waves. 1 hz = 1 cycle per second.
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Decibel
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A unit of sound intensity level
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Compression
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The region of a longitudinal wave in which the vibrating particles are closer than their equilibrium distance.
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Rarefaction
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The region in a longitudinal wave where vibrating particles are farther apart than the equilibrium distance.
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Beats
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When two notes of slightly different frequencies reach the ear at the same time. A burst of sound followed by silence
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Constructive Interference
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When two waves make the medium vibrate in the same direction they reinforce and make a bigger disturbance
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Destructive Interference
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When two waves make a medium vibrate in opposite directions, they tend to cancel each other. This will result in a smaller wave or one that disappears completely.
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Doppler Effect
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When there is relative motion between a source of a wave and an observer, the frequency of vibrations received by the observer increases if the source and observer approach each other and decreases when the source and observer distance is increasing. Ex, the pitch of a siren changes as it approaches and passes you.
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Law of Reflection
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When a wave is reflected, the angle of incidence equals the angle of reflection.
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Regular Reflection
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from smooth flat surfaces, incident waves in the same plane are reflected in the same plane. Ex. A plane mirror
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Diffuse Reflection
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from rough and irregular surfaces, reflected light waves go in many directions. Ex. A piece of paper.
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Concave Mirror
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Reflecting surface is the inside of a spherical shell
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Convex Mirror
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Reflecting surface is the outside of a spherical shell
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Equation for focal length of a spherical mirror
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f=R/2; R=radius of the spherical shell; f=focal length
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Angle of Incidence
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Angle between the incident light and the normal to the reflecting surface
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Angle of Reflection
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Angle between the reflected light ray and the normal to the reflecting surface
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Refraction
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The bending of a wave on going into a second medium; eg, a light wave bends when going from air to water
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Critical Angle
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The limiting angle of incidence in the optically denser medium that results in an angle of refraction of 90 degrees
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Snell's Law
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Snell's Law
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Convex Lens
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A convex lens is thicker in the middle than at the edges; it is also called a converging lens
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Concave Lens
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A concave lens is thinner in the middle than at the edges; it is also called a diverging lens.
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Focal Length
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The distance from the principal focus to the lens or mirror
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Index of Refraction
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A measure of the angle or degree an electromagnetic wave bends when travelling from one substance to another. Ex. Put a pencil in a bowl of water, the pencil will appear bent because the light waves bend when going from water to air.
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Lens Equation
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1/p + 1/q = 1/r; p=object distance; f=focal length; q=image distance
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Equation relating object and image sizes for lens.
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Equation relating object and image sizes for lens.
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Equation for telescopic magnification
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Equation for telescopic magnification
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Huygen's Principle
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Each point on a wave front may be regarded as a new source of disturbance
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Diffraction
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the bending of a wave around obstacles
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Polarized Light
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Light whose direction of vibration has been restricted into one plane of vibration
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Virtual Image
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A mirror or lens image formed by the eye and brain which can not be projected on a screen. Ex, the image you see of yourself in the mirror
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Equation for the Focal Length of a spherical mirror of radius R
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F=R/2; F=focal length; R=radius
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Formula for the Index of Refraction
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Formula for the Index of Refraction
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Formula for Coulomb's Law
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Formula for Coulomb's Law
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Equation for Electric Field Intensity
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E = F/Q; E=electric field intensity; F= force exerted; Q=charge
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Equation for Potential Difference between two points
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V=W/Q; V=voltage (volts); Q=charge (coulombs); W=work (joules)
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Parallel Circuit
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Where resistors in a circuit are connected independent of each other. Circuit is in the form of several loops.
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Series Circuit
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Where resistors are connected so that the current flows from the tip of one to the tail of another
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Formula for Current in a series circuit (Ohm's Law applied)
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Formula for Current in a series circuit (Ohm's Law applied)
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Formula for current in a parallel circuit (Ohm's Law applied)
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Formula for current in a parallel circuit (Ohm's Law applied)
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Formula for Resistance in a series circuit (Ohm's Law applied)
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Formula for Resistance in a series circuit (Ohm's Law applied)
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Formula for Resistance in a parallel circuit (Ohm's Law applied)
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Formula for Resistance in a parallel circuit (Ohm's Law applied)
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Formula for voltage in a series circuit (Ohm's Law applied)
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Formula for voltage in a series circuit (Ohm's Law applied)
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Formula for voltage in a parallel circuit (Ohm's Law applied)
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Formula for voltage in a parallel circuit (Ohm's Law applied)
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Formula for Ohm's Law
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V = IR; V=voltage in volts; I = current in amperes; R=resistance in ohms
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Law of Magnets
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Like poles repel, unlike poles attract. North repels north; south repels south; north attracts south
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Magnetic Field
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The region where a magentic influence can be detected as a force on a magnet
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Left-Hand Rule
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Grasp the wire with the left hand so that the thumb will point in the direction of the electron flow; fingers will then direct towards flux lines.
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Electromagnet strength depends upon which three things
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1) The number of turns in the coil of the solenoid; 2) the nature of the core; 3) The current through the core.
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Galvenometer
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Instrument which measures low values of current.
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Voltmeter
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an instrument calibrated to measure the potential difference connected to its terminals.
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Alternating Current (AC)
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Current whose direction is constantly reversing. This is the type of current you get from the wall outlet.
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Direct Current (DC)
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Current whose direction is one path, never reversing. This is the type of current you get from a battery.
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Inertia
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Tendency of an object to remain in its present state of motion
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Mass
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Quantitative measure of an object's inertia
How much that object will resist a change in motion Measure in kilograms (kg) |
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Weight
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Gravitational force an object experiences when near a much larger body of mass
Measured in newtons (N) Weight = mg Weight and mass are proportional, but are not the same physical quantity |
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Center of mass
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Single point of an object where mass is concentrated
Point through which a single force may be applied in any direction causing object to accelerate equally Does not always coincide with geometric center |
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Center of gravity
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Single point at which the force of gravity can be applied to the entire mass
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4 Forces in nature:
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1. Strong nuclear forces
2. Weak nuclear forces 3. Gravitational force 4. Electromagnetic force Only last 2 forces are tested on the MCAT |
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Contact forces
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Must act in at least 1 of 2 directions:
1. Perpendicular to surface (normal force) 2. Parallel to surface (requires friction) Exception is tension, which can act in any direction away from object Considered electromagnetic forces Something must be making visible contact with system Not do act at distance |
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Gravitational force
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F = mg
Act at distance |
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Electromagnetic force
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Requires charged object or a magnet
Act at distance |
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Newton's 1st law
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Law of inertia
An object in a state of rest or in a state of motion will tend to remain in that state unless it is acted upon by a net force |
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Newton's 2nd law
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F = ma
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Newton's 3rd law
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For every action there exist an equal and opposite reaction
Forces never act on same system |
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Newton's law of universal gravitation
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Every mass in the universe exerts an attractive force on every other mass in the universe
F = Gm1m2/r^2 G = 6.67e^-11 m^3 kg^-1 s^-2 Gives magnitude of force but not direction |
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Normal force (Fn)
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Force perpendicular to surface
Force of inclined plan pushing back against gravitational force Normal force of inclined plane: Fn = mgcos0 Normal force of curved surface: Fn = mgcos0 + mv^2/r (centripetal force) |
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Net force of incline plane (no friction)
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Fnet = mg + Fn
Fnet = mgsin0 Points directly along inclined plane |
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Circular motion
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Object spinning or moving in circles
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Centripetal acceleration
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Ac = v^2/r
Always points toward the center of circle that is circumscribed by motion Direction is always changing Magnitude is always constant |
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Centripetal force
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Fc = mv^2/r
Always points toward center of circle Must be created by another force Must be at least one of three forces: 1. Gravity 2. Electromagnetic 3. Contact |
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Acceleration down inclined plane
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a = gsin0
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2 Directions of contact force:
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1. Normal force (Fn) is always perpendicular to contact surface
2. Frictional force is always parallel to contact surface |
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Friction
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Cause by attractive molecular forces between contiguous surfaces
Opposes relation motion between surfaces |
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2 types of friction:
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1. Static friction (Fs)
2. Kinetic friction (Fk) |
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Static Friction
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Force opposing motion when 2 contiguous forces are not moving relative to each other
No sliding Fs = uFn |
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Kinetic Friction
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Force resisting motion once the 2 contiguous surfaces are sliding relative to each other
Yes sliding Fk = uFn |
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Coefficients of friction (u)
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Represent fractions of normal force that will equal static and kinetic frictional forces
Usually have a value less than 1 u(static) is greater than u(kinetic) |
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Drag
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Air resistance
Type of friction Fluid resistance to an object's motion through that fluid |
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Viscosity
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Type of friction
Fluid's resistance to motion through itself |
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Tension
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Force acting through a flexible object with no mass, such as a string or rope
Equal throughout rope as long as there is no friction acting on the rope At any point in rope, there is tension force pulling in equal and opposite directions, but only use force pulling away from system Replace rope with force vector acting on system |
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Hooke's Law
|
Force due to a compressed or stretched object
Force applied by most objects against a deforming force F = -k(Xf - Xi) Negative sign can usually be ignored Usually refers to springs |
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Equilibrium
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No translational (straight line) or angular (rotational) acceleration
All velocities are constant Does not mean motionless Sum of all forces acting on system equal to zero (ie. Net Force = 0) Fup = Fdown Fright = Fleft |
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Static Equilibrium
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If all velocities are zero
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Dynamic Equilibrium
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If all velocities are constant and nonzero
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Translational Equilibrium
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Upward forces equal downward forces and rightward forces equal leftward forces
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System not in equilibrium
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Center of mass of system is accelerating translationally or its parts are accelerating rotationally
Sum Forces = ma 1. Write equations as if system in equilibrium 2. Add "ma" to side with less force (all numbers should be positive) |
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Torque
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Twisting force, clockwise or counterclockwise
T = Frsin0 F: force r: position (distance from point of rotation to point of application of force) T = Fl F: force l: lever arm 0: angle between force and position vectors |
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Point of Rotation
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Any fixed point of your choosing
Center of mass |
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Lever arm (l)
|
Position vector is from point of rotation to point where force acts at 90 degress
T = Fl |
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How to solve Torque problems:
|
1. Fup = Fdown
2. Fright = Fleft 3. Tclockwise = Tcounterclockwise |
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Energy
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Capacity to do work
Units: 1. joules (J) = kg m^2/s^2 2. electron-volt (eV) Scalar 2 types: 1. mechanical 2. nonmechanical |
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Mechanical Energy
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Kinetic energy and potential energy of macroscopic systems (system you can examine without a microscope)
|
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Kinetic Energy (K)
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Energy of motion
Any moving mass has kinetic energy K = (1/2)mv^2 |
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Potential Energy (U)
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Energy of position
Several types: 1. gravitational potential energy (Ug) 2. elastic potential energy (Ue) 3. electric potential energy (Uelectric) |
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Gravitational Potential Energy (Ug)
|
Energy due to force of gravity
Ug = -Gm1m2/r G: universal gravitational constant m1 & m2: 2 masses r: distance from 2 centers of gravity neg sign: indicates energy decreases as distance decreases |
|
Gravitational Potential Energy near Earth's surface
|
Ug = mgh
m: mass g: gravity h: height of object |
|
Elastic Potential Energy (Ue)
|
Energy due to resistive force applied by deformed object
Follows Hooke's Law Ue = (1/2) k (change in x^2) k: Hooke's law constant change in x: displacement of object from relaxed position |
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Law of Conservation of Energy
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Since universe is an isolated system (mass nor energy is exchanged with environment), the energy of universe remains constant
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2 types of energy transfer:
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1. work (W)
2. heat (Q) |
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Work
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Transfer of energy via a force
Scalar Measured in units of energy (joules) W = Fdcos0 (for all forces except friction) F = force d = displacement 0 = angle between F & d |
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Heat (Q)
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Transfer of energy by natural flow from a warmer body to a colder body
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Frictional Force
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Change internal energy as well as mechanical energy
Therefore are not forces which can do work |
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Work = forces & no heat
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W = (change in K) + (change in U) + (change in Ei)
Ei = internal energy, frictional energy |
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W = forces & no heat & no friction
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W = (change in K) + (change in U)
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Work-Energy Theorem
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W = (change in K)
Only true when all energy transfer results on in change of K |
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1st Law of Thermodynamics
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Energy is always conserved
Change in E = W + Q |
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Conservative Force
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Mechanical energy is conserved within system. Net Work = zero.
Has potential energy associated with them Types: 1. gravitational forces 2. hooke's law forces 3. electrical forces 4. magnetic field forces |
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Law of conservation of mechanical energy
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When only conservative forces are acting, the sum of mechanical energies remains constant
K1 + U1 = K2 + U2 (no heat, only conservative forces) 0 = (change in K) + (change in U) (no heat, conservative forces only) |
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What work is done by a conservative force?
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Consider conservative force is not part of system
1. W = Fdcos0 2. Calculate change in Ug 3. W = (Change in K) + (Change in U) + (Change in Ei) (do not include calculation of conservative force being questioned) Technically conservative forces do not do work because energy is never lost no gained by system |
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Nonconservative forces
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Forces that change mechanical energy of a system when they do work
types: 1. kinetic frictional forces 2. pushing and pulling forces W = (change in K) + (change in U) (except for frictional forces, no heat) |
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Kinetic frictional forces
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Increase internal energy of systems to which applied
Amount of work done by such a force does not go into changing mechanical energy W = (Change in K) + (change in U) = (Change in Ei) K = Ei |
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Power
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Rate of energy transfer
Unit: watt (W) = J/s P = (change in E)/t (E: energy = W + Q) Rate at which force does work P = W/t (work /time) |
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Instantaneous Power due to Force
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P = Fvcos0
0: angle between F & v v: velocity F: force Scalar |
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Momentum (p)
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measure of a moving object's tendency to continue along its present path. closely related to inertia
p = mv (mass * velocity) in kg m/s 1. in an isolated system, momentum is always conserved 2. momentum is a vector initial momentum of an isolated system is always equal to final momentum in magnitude and direction M1V1 = M2V2 |
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Elastic collisions
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--- mechanical energy is conserved
--- no energy dissipates to internal energy --- example is atomic collisions --- conservation of mechanical energy --- Uinitial + Kinitial = Ufinal + Kfinal |
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Inelastic collisions
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--- lose some mechanical energy to internal energy
--- must use conservation of momentum to solve inelastic collision probelms --- Pinitial = Pfinal completely inelastic collision stick together M1V1 + M2V2 = (M1+M2)V3 Px (initial) = Px (final) Py (initial) = Py (final) |
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Reverse collisions
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--- Objects start together and suddenly burst apart
--- Final and initial momentum are equal --- Example is explosion or radioactive decay where species start from rest --- in a 2 piece explosion, 2 pieces must separate in exactly opposite directions because of vector nature of momentum M3V3 = M1V1 + M2V2 M1V1 = M2V2 |
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Impulse (J)
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--- equal to change in momentum
--- J = change in momentum --- Force during time of collisions is not constant --- Average force: --- J = (Favg)(change in time) --- Change in p = (Favg)(change in t) --- If time over which collision occurs is increased, than force is decreased |
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Machines
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mechanical devices that reduce force when doing work
ideal machines reduce force but don't change work nonideal machines increase work because they increase internal energy through friction 3 machines: 1. ramp 2. lever 3. pulley |
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Ramp
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W = mgh
work =mass*gravity*height F = mgsin0 fraction by which we reduce the force must be equal to fraction by which we increase the length of the ramp work is not changed |
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Lever
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based on principle of torque
increases distance through which force acts clockwise torque must equal counter-clockwise torque T = Fl torce=force * lever arm work is not changed |
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Pulley
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based on principle of ramp and lever
allows force to act on a greater distance and thus do same amount of work with less force tension through a massless rope attached to a frictionless, massless pulley is constant tension is the same at every point in the rope |
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Radioactive Decay
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concerns atoms that spontaneously break apart
hydrogen does not undergo spontaneous decay No atoms with more than 83 protons are considered stable 5 types: 1. alpha decay ---- 2. beta decay 3. positron emission (beta decay) 4. gamma ray production 5. electron capture (beta decay) |
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Half-life
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--- predictable rate of decay of any substance (large group of identical atoms)
--- of time necessary for 1/2 of given amount of substance to decay --- 4 variables: 1/2. initial and final amount of substance 3. # of half-lives (time period/half-life) 4. length of half-life |
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Alpha decay
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alpha particle is a helium nucleus = 2 protons and 2 neutrons
an alpha particle is lost mass number (A) decreases by 4 atomic number (Z) decreases by 2 |
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Beta decay
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expulsion of an electron
beta particle is an electron or a positron (an electron with a positive charge) not the destruction of an electron, instead it is the creation of an electron and a proton from a neutron and the expulsion of the newly created electron mass number (A) doesn't change atomic number (Z) increases by 1 |
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Positron emission
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--- type of beta decay
--- emission of a positron when a proton becomes a neutron --- a proton is transformed into a neutron and a positron is emitted --- mass number (A) doesn't change --- atomic number (Z) decreases by 1 |
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Electron capture
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capture of an electron along with the merging of that electron with a proton to create a neutron
a proton is destroyed and a neutron is created mass number (A) doesn't change atomic number (Z) decreases by 1 |
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Gamma ray production
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--- high frequency photon
--- has no charge and doesn't change the identify (atomic number, Z) of the atom from which it is given off --- often accompanies other decay types when an electron and a positron collide --- mass number (A) and atomic number (Z) doesn't change --- matter-antimatter collision (annihilation), where mass is destroyed releasing energy in the form of gamma rays |
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Rest mass energy
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E = mc^2
E: energy m: mass created or destroyed c: speed of light (3e^8 m/s) latent energy within the mass of an object use when mass is created or destroyed |
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Mass defect
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difference in masses before and after creation or destruction of mass
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Fusion
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combining of 2 nuclei to form a single heavier nucleus
binding energy increases, new bonds are more stable and stronger large amount of energy is released, energy comes from mass defect more energy was released in formation of stronger bonds than was absorbed in breaking of weaker bonds |
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Fission
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splitting of single nucleus to form 2 lighter nuclei
large amount of energy is released, energy comes from mass defect |
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Fluid
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---- liquid or gas
---- molecular bonds are constantly breaking and reforming due to high KE of molecules ---- molecules not arranged in any order or structure, move about in random directions, therefore has only temporal resistance to forces that are not perpendicular to its surface ---- can create permanent force outward, allowing resistance to forces perpendicular (normal) to surface |
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Density (p)
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--- heaviness of a fluid
--- how much mass it contains in a specified volume --- p = m/V p: density (kg/m^3) --- intrinsic property, amount of substance will not change density --- assume all liquids and solids are totally incompressible, meaning constant density --- gases change their volume, and thus their density as per PV=nRT |
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Specific gravity (S.G.)
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density of that substance compared to density of water
S.G. = p(substance)/p(water) < 1: lighter than water = 1: equally heavy as water > 1: heavier than water |
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Density of water
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p(water) = 1000 kg/m^3
p(water) = 1 mg/cm^3 |
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Fluid pressure
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pressure experience by object as result of fluid
results from impulse of molecular collisions P = F/A P(fluid pressure (pascals, Pa)) = F(avg force of collisions) * area scalar, no direction exists in fluid whether or not object is immersed in fluid measure of KE due to random velocities of molecules within fluid distributed over fluid volume type of stored energy per unit volume |
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Fluid at rest
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--- experiences only forces perpendicular to its surface, --- normal force and gravitational force
--- fluid at rest, uniform density, sealed container P = pgy P(fluid pressure) = p(density) * gravity * y(fluid depth) --- additional fluids on top of 1st fluid, add their weight Ptotal = p1gy1 + p2gy2 + p3gy3 --- open container, must add atmospheric pressure to fluid P = pgy + P(atm) P(atm) = 101,000 Pa |
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Gauge pressure
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measure of pressure compared to local atmospheric pressure (given value of zero)
example: negative pressure created in your chest when you breathe, higher Patm pushes air into lungs suck through a straw, create vacuum inside straw and Patm pushes down on fluid outside straw, pushing fluid up inside straw |
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Absolute pressure
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pressure measured relative to a vacuum (zero)
Pabs = Pgauge + Patm |
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Pascal's principle
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pressure applied anywhere to an enclosed incompressible fluid, will be distribute undiminished throughout fluid
does not apply to gas, because gas is compressible |
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Hydraulic lift
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machine that works via Pascal's principle
does not change work, but decreases distance through which force is applied piston 1 applies P to incompressible fluid, which transfers to piston 2 undiminished, since piston 2 has greater area than piston 1, force on piston 2 is greater |
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Archimede's principle
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object submerged in fluid displaces volume of fluid equal to its own volume
buoyant force is an upward force acting on submerged object and is equal to weight of fluid displaced by submerged object |
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Buoyant force
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before submerged, upward force on fluid that it will displace must equal weigh of fluid
Fb = mg(water) upward force acts on submerged object Fb = p(fluid)Vg Fb(buoyant force) = p(density of fluid) * (volume displaced) * (gravitational constant) due to difference in pressure, therefore doesn't change with depth fully submerged object displaces its volume in fluid |
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Floating object
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displaces amount of fluid equal to its own weight
submerged fraction of floating object equals ratio of object density to fluid density in which object is floating if in water, ratio is S.G. of floating object Fraction submerged = p(object)/p(fluid) floating object displaced its weight in fluid |
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Center of buoyancy
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point where buoyant force acts
point where center of mass would be if object had uniform density if center of mass and center of buoyancy do not coincide (object is not uniformly dense) then torque will result and cause object to spin |
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molecules of moving fluid
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1. random translational motion
2. uniform translational motion |
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Random translational motion
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contributes to fluid pressure as in a fluid at rest
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Uniform translational motion
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shared equally by all molecules at a give location in a fluid
motion of fluid as a whole doesn't contribute to fluid pressure |
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ideal fluid
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1. no viscosity (tendency to resist flow)
2. incompressible, uniform density, constant volume 3. no turbulence, steady flow, same velocity 4. irrotational flow, object moving with fluid will not rotate 5. constant Q (flow rate) |
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Continuity equation
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Q = Av
Q: volume flow rate = rate at which volume passes through pipe A: cross-sectional area of pipe v: velocity of fluid flow, v = d/t |
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Bernoulli's equation
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K = P + pgh + 1/2pv^2
K: constant specific to fluid P: pressure h: height v: velocity p: density given one continuous ideal flow, the sum of its 3 terms is a constant at any point in the fluid describes conservation of energy within an ideal fluid |
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Direction of fluid flow
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Change P = QR
P: pressure Q: flow rate R: resistance to flow |
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surface tension
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intensity of intermolecular forces per unit length
reason why needle (more dense) floats on surface of water not buoyant force because no water is displaced responsible for formation of water droplets higher the temperature, weaker the surface tension because less intermolecular forces |
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Capillary action
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fluid is pulled up a thin tube
1. intermolecular forces responsible for surface tension (cohesive forces) 2. forces between molecules of tube and fluid (adhesive forces) > cohesive forces = convex & fluid pulled down > adhesive forces = concave & fluid pulled up |
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Stress
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force applied to object divided by area over which force is applied
same units as pressure (N/m^2, not Pa) Stress = F/A done to an object |
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Strain
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fractional change in object's shape
ratio of change in dimension compared to original dimension no units Strain = change dimension/original dimension how object responds to stress |
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Modulus of elasticity
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stress and strain are proportional to each other
Modulus of elasticity = stress/strain up to a max (yield point, still intact, deformation), modulus of elasticity is constant for specific substance fracture point, object breaks |
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3 types of moduli
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1. young's modulus (E)
2. shear modulus (G) 3. bulk modulus (B) |
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Young's modulus (E)
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tensile stress
E = (F/A)/(change h/h) h: height |
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Shear modulus (G)
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shear stress
G = (F/A)/(change x/h) x: length h: height |
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Bulk Modulus (B)
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compression and expansion
B = (change P)/(change V/V) P: pressure V: volume |
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Equations for fluids at rest
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p = m/V
P = F/A S.G. = p(substance)/p(water) P = pgy Fb = pVg |
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Equations for fluids in motion
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Q = Av
K = P + 1/2pv^2 + pgh v = square root (2gh) |
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Equations for Solids
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Modulus of elasticity = stress/strain
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wave
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transfer of momentum and energy from one point to another
3 types: 1. mechanical 2. electromagnetic 3. matter |
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Mechanical waves
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obey law of classical physics
require some medium through which to propogate non dispersive medium is momemtarily displaced by wave and then returned to its position 2 types: 1. transverse wave 2. longitudinal wave |
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transverse wave
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medium is displaced perpendicularly to direction of wave propagation
ex: wave on a string can be represented by sine function (vertical displacement of medium with respect to time or displacement of wave) |
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longitudinal wave
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medium displaced parallel to direction of wave propagation
ex: sound wave in air can be represented by sine function (change in pressure or horizontal displacement of medium with respect to time or displacement of wave) |
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wavelength
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if x-axis is displacement of wave, it is measured from any point in wave to point where wave begins to repeat itself
ex: trough to trough or peak to peak units of meters |
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wave
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transfer of momentum and energy from one point to another
3 types: 1. mechanical 2. electromagnetic 3. matter |
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Mechanical waves
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obey law of classical physics
require some medium through which to propogate non dispersive medium is momemtarily displaced by wave and then returned to its position 2 types: 1. transverse wave 2. longitudinal wave |
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transverse wave
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medium is displaced perpendicularly to direction of wave propagation
ex: wave on a string can be represented by sine function (vertical displacement of medium with respect to time or displacement of wave) |
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longitudinal wave
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medium displaced parallel to direction of wave propagation
ex: sound wave in air can be represented by sine function (change in pressure or horizontal displacement of medium with respect to time or displacement of wave) |
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wavelength
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if x-axis is displacement of wave, it is measured from any point in wave to point where wave begins to repeat itself
ex: trough to trough or peak to peak units of meters |
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frequency (f)
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number of wavelengths that pass a fixed point in 1 second
measured in hertz (Hz) or cycles/sec (1/s) |
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velocity
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product of wavelength and frequency
v = wf dictated by medium through which wave travels change in frequency or wavelength does not change velocity of wave |
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period (T)
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reciprocal of frequency
number of seconds required for 1 wavelength to pass a fixed point where x-axis is time, any point on wave to next point where wave begins to repeat itself T = 1/f |
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amplitude (A)
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maximum displacement from zero
always positive |
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medium
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only thing that affects velocity
1. medium's resistance to change in shape (elasticity) 2. medium's resistance to change in motion (inertia) for a gas, velocity always increases with temperature elastic component stores PE inertial component stores KE |
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intensity (I)
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power of waves
rate at which waves transfer energy units of W/m^2 proportional to A^2 and f^2 |
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decibels (dB)
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dB = 10log (I/Io)
dB: decibels I: intensity Io: threshold intensity of human hearing I > 10X, dB > 10 I > 10^2, dB > 20 I > 10^3, dB > 30 I > 10^4, dB > 40 ex: I > from 30 to 3000, dB > 20 (added 2 zeros to I, so add 20 to dB) |
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phase
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relates to its wavelength, frequency, place and time of origin
horizontal shift of a wave on a graph in phase: same wavelength & begin at same point out of phase: same wavelength & different distances but arrive at same point |
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constructive interference
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waves occupy same space and superposition occurs
sum of displacements results in greater displacement |
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destructive interference
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occurs when sum of displacements results in smaller displacement
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beats
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2 waves with slightly different frequencies are superimposed
at some points waves will experience constructive interference and at others destructive interference points will alternate with frequency equal to difference between frequencies of original 2 waves alternating increase and decrease in noise intensity pitch correlates to frequency: high note = high pitch = high frequency fbeat = |f1 - f2| |
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wave reflection
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if wave reflects off denser medium, wave is inverted
if wave reflects off less dense medium, wave is upright when wave reflects from 1 medium to the next, wavelength changes but frequency remains the same |
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Node
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2 waves traveling in opposite directions with same wavelength, point of intersection has zero displacement
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antinode
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2 waves traveling in opposite directions with same wavelength, point of maximum constructive interference, greatest amplitude
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standing wave
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string holds still at nodes and moves violently up and down at antinodes
endless sine waves, with same wavelength, traveling in opposite directions |
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harmonic series
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list of wavelengths from largest to smallest of possible standing waves
harmonics are number from longest to shortest wavelength |
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1st harmonic (fundamental wavelength)
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longest wavelength
created with fewest number of nodes = 2 distance from 1 wall to other is 1/2 wavelength each successive harmonic is created by adding a wavelength |
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pipe open or closed at both ends or string tide at both ends
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L = (nfn)/2 (n= 1, 2, 3, etc)
L: distance between 2 ends of string n: number of harmonic both ends are nodes |
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pipe open or closed at 1 end or string tide at 1 end
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L = (nfn)/4 (n= 1, 3, 5, etc)
L: distance between 2 ends of string n: number of harmonic one end is an antinode |
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resonate
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--- standing waves cause string to resonate
--- vibrate at its natural frequency or resonant frequency --- v = fw (velocity = resonant frequency * wavelength) --- velocity is constant for a given medium --- at resonant frequency, structure experiences maximum vibration velocities and displacement amplitudes |
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resonance
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situation where natural frequency and driving frequency are equal
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simple harmonic motion
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- sinusoidal function
- acceleration is proportional to displacement but opposite in sign - acceleration and displacement are related by f^2 - oscillation between KE and PE, no energy is lost to surroundings - ex: mass bouncing on end of massless spring OR pendulum swinging at a small angle OR plant's orbit WACK'EM: w = square root (k/m) angular frequency for mass on a string WIGGLE: w = square root (g/L) angular frequency for pendulum |
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doppler effect
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results because waves are unaffected by speed of source with produces them
(change f/fs) = v/c frequency/frequency source = (relative velocity) * (wave velocity (change w/ws) = v/c wavelength |
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Wave equations
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v = fw
T = 1/f |
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Sound equations
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dB = 10log(I/Io)
fbeat = |f1 - f2| L = (nwn)/4 (n= 1, 3, 5, etc) L = (nwn)/2 (n= 1, 2, 3, etc) |
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Doppler effect equations
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(fo - fs)/fs = v/c
(wo - ws)/ws = v/c |
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charge
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--- positive and negative charge
--- current runs in opposite direction of electrons --- charge = q (units of coulombs C) --- it is quantized, which means any charge must be at least as large as certain smallest unit --- smallest unit of charge, e = 1.6e-19 C = charge of 1 electron or proton --- opposite charges attract each other, like charges repel each other |
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universal law of conservation of charge
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universe has zero net charge
net charge is created by separating electrons from protons anytime a positive charge is created, a negative charge is created as well |
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Coulomb's law
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formula describing magnitude of force of repulsion or attraction between 2 charged objects
analogous to gravitation force formula F = kq1q2/r^2 k: coulomb constant = 8.988e9 q: respective charges r: distance between centers of charge force due to gravity is negligible compared to force due to charge |
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center of charge
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point from which charge generated by object or system can be considered to originate
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field
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man-made concept designed to explain action at a distance
forces created by fields can act at a distance |
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lines of force
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--- can represent any field
--- lines point in direction of field --- positive to negative for electric field --- towards the mass creating the field for gravitational fields --- relative distance between lines indicate strength of field --- no lines of forces inside a uniformly charged sphere |
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electric field (E)
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electrostatic force per unit charge
vector point in direction of field units of N/C or V/m |
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electric field of point charge
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E = kq1/r^2
system of point charges: summing (vector addition) of each electric field for each charge |
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force on charge in electric field
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F = Eq
F: force E: electric field q: charge |
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potential energy (U) of charge in electric field
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U = Eqd
U: potential energy E: electric field q: charge d: displacement |
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electric potential energy
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U = kq1q2/r
U: electric potential energy k: coulomb constant q: charge r: distance between charges |
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voltage (V)
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potential of the field
potential for work by an electric field in moving any charge from 1 point to another V = Ed V: voltage (volts, V), scalar or J/C E: electric field d: displacement |
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voltage due to point charge
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V = kq1/r
voltage due to group of point charges: voltage due to each individual charge is summed directly |
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work due to electric field
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W = mgh
W = qEd |
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equipotential surfaces
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all points are same voltage
surface normal to field that describes set of points all with same potential |
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electric dipole
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created by 2 opposite charges with equal magnitude
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conductors
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allow electrons to flow relatively freely
good conductors of electricity, poor resistors such as metals |
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resistors
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poor conductors
hold electrons tightly in place such as: networks solids such as diamond and glass |
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induction
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ability to charge a conductor because of easy flow of electrons
1. if negatively charged object is moved close to electrically insulated conductor, electrons on conductor will repel to opposite side 2. touch conductor with 2nd conductor, electrons will repel further and move to 2nd conductor 3. remove 2nd conductor, 1st conductor has less electrons than protons (induced positive charge) |
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current
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moving charge
given in amps (A) or C/s scalar, flow in direction of movement of positive charge because electrons were designated as negative charge, current created by flowing electrons is in opposite direction of flow of electrons flow of electrons resembles fluid flow |
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circuit
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cyclical pathway for moving charge
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resistivity (p)
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quantitative measure of property that all substances resist flow of charge
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resistance (R)
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quantitative measure of an object of a particular shape and size to resit flow of charge
measured in ohms |
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Ohm's law
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product of resistance and current
V = IR V: voltage (gh) I: current R: resistance |
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Kirchoff's 1st rule
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amount of current flowing into a node must be same amount that flows out
rate at which fluid flows into an intersection much match rate at which fluid flows out |
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node
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any intersection of wires
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kirchoff's second rule
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voltage around any path in a circuit must sum to zero
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electromotive force (EMF)
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not a force, but instead voltage provided by battery
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capacitor
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used to temporarily store energy in a circuit
stores it in the form of separated charges |
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parallel plate capacitor
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2 plates made from conductive material are separated by a very small distance
on a charged capacitor, 1 plate holds positive charge and the other holds same amount of negative charge separation of charge creates electric field that is constant |
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capacitance
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ability to store charge per unit voltage
something with high capacitance can store a lot of charge at low voltage C = Q/V C: capacitance Q: charge of plate V: votlage |
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energy stored by capacitor
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U = 1/2QV
U = 1/2CV^2 U = 1/2Q^2/C U: energy stored Q: charge V: voltage C: capacitance |
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dielectric constant (K)
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acts to resist creation of electric field, allowing capacitor to store more charge (greater capacitance)
higher K means greater capacitance Kvacuum = 1 limits value of possible voltage across plates, at max voltage K will breakdown and conduct electricity work is done on K and energy is stored in K |
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Series
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components lined up in row, like train cars
any 2 components not separated by a node |
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parallel
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single components in alternate paths connecting same node
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resistor in series
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total resistance (effective resistance, Reff) is sum of resistances
Reff = R1 + R2 + R3 + ... |
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Resistor in parallel
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1/Reff = 1/R1 + 1/R2 + 1/R3 + ...
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Capacitors in series
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1/Ceff = 1/C1 + 1/C2 + 1/C3 +...
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Capacitors in parallel
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Ceff = C1 + C2 + C3 + ...
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Power
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same quality as mechanical power
P = IV P = I^2R P = V^2/R rate at which heat is generated by current as it flows through resistor is equal to power dissipated |
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Direct current (DC current)
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net movement of electrons is in one direction around circuit
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Alternating current (AC current)
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created by oscillating electrons back and forth in simple harmonic motion
voltage or current can be described by sine wave since movement of electrons creates power regardless of direction, electrons do not have to be driven in one direction current commonly used in home outlets |
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Max current
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occurs when electrons are at max velocity
Imax = square root (2Irms) Imax: max current Irms: root mean square current |
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Max voltage
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Vmax = square root (2Vrms)
Vmax: max voltage Vrms: root mean square voltage |
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RMS
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root mean square
square root of average of squares square all terms, take average, then take square root average value of sine wave = 0 Vrms = 120V --> Vmax = 170V |
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magnetic fields (B)
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--- generated by moving charge, which experiences force when moving through a magnetic field
--- similarities to electric fields, measured in units of Telsa (T) --- north and south poles; like poles repel and opposite poles attract, poles never exist separately --- can be represented by lines of force, point from N to S pole (earth's magnetic field points in opposite direction) |
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Right hand rule (RHR)
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predicts direction of magnetic field due to current carrying wire
thumb: direction of current fingers: grab wire, direction in which fingers wrap around wire is direction of magnetic field |
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force experience by charge moving through magnetic field
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F = qvBsin0 = mv^2/r (find radius of curvature)
F(force) = q(charge) * v(velocity) * (B)magnetic field) * sin 0( angle between magnetic field and velocity) --- force is directed perpendicularly to both velocity and magnetic field, therefore does not work, leaving only 2 possible directions for force --- RHR thumb: direction of moving positive charge fingers: direction of magnetic field palm: direction of force negative charge reverses direction of force |
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Faraday's law of induction
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a changing magnetic flux induces an EMF (E) and a current, which creates an induced magnetic field
forces due to induced electric field (EMF) are nonconservative, thus mechanical energy is transferred to internal energy |
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Lenz's law
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induced current will create a magnetic field opposing induced magnetic field
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electric fields due to point charge equations
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F = kq1q2/r^2
U = kq1q2/r E = kq1/r^2 V = kq1/r |
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constant electric fields equations
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F = Eq
U = qEd = Fd = Vq V = Ed |
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Resistors equations
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V = IR
P = IV P = I^2R P = V^2/R Series: Reff = R1 + R2 +... Parallel: 1/Reff = 1/R1 + 1/R2 +... |
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Capacitors equations
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C = Q/V
U = (1/2)QV U = (1/2)Q^2/C U = (1/2)CV^2 Series: 1/Ceff = 1/C1 + 1/C2 +... Parallel: Ceff = C1 + C2 +... |
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AC current equations
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Vmax = square root (2Vrms)
Imax = square root (2Irms) |
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magnetism equations
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F = qvBsin0
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Electromagnetic wave
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traveling oscillation of an electric and a magnetic field
fields are perpendicular to each other and directions of propagation is perpendicular to both fields it is a transverse wave generated by acceleration of electric charge |
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Speed of electromagnetic wave (c)
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constant speed and always equal to ratio of magnitudes of electric field and magnetic field
c = E/B energies of 2 fields are equal |
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Poynting vector (S)
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describeds the rate and direction in which an electromagnetic wave is transporting energy per unit area
always perpendicular to both E and B has a magnitude of EBsin0 |
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Light
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tiny sliver from the electromagnetic spectrum
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visible light
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includes wavelengths from 390 to 700 nm
shorter wavelengths correspond to violet light and longer wavelengths to red light |
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ultraviolet light
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just beyond visible spectrum on smaller wavelength side
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infrared
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just beyond visible spectrum on longer wavelength side
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colors of visible spectrum
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Roy G. Biv
Red, orange, yellow, green, blue, indigo, violet wavelengths toward violet have more energy |
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index of refraction (n)
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constant for the medium light propagates through
n = c/v n( index of refraction) = c(speed of light in vacuum) / v(speed of light in medium) --- since nothing exceeds the speed of light in a vacuum, all media have an index of refraction greater than 1 --- the greater the index of refraction, the slower light moves through that medium n for water = 1.3 n for glass = 1.5 |
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plane-polarized light
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light with electric fields in one particular direction as a result of screening out photons not have an electric field in one particular direction (filter)
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isotropic light
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unpolarized light, white light
electric fields point in all directions when polarized, it loses 1/2 of its intensity |
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dual nature
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acts both as a wave and a particle
propagation properties can be described with wave theory energy transformation properties are best described by particle theory |
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angle of incidence
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angle at which light ray strikes the interface as measured from a line normal to the interface
equals angle of reflection |
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angle of reflection
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angle at which light ray reflects off of interface as measured from a line normal to the interface
equals angle of incidence |
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angle of refraction
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angle at which light ray refracts through the interface as measured from a line normal to the interface
given by Snell's law: n1sin01 = n2sin02 |
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Snell's law
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gives you angle of refraction
n1sin01 = n2sin02 |
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Energy of a single photon
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E = hf
E: energy of single photon h: planck's constant f: frequency when light crosses into a new medium, frequency remains the same and wavelength changes |
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total internal reflection
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occurs when light coming from a medium with higher index of refraction, causes angle of incidence to be so large that entire amount of photons will be reflected at the angle of reflection and none will refract
this angle of reflection is the critical angle |
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critical angle
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angle at which light reflects when there is total internal reflection (no refraction)
0critical = sin^-1(n2/n1) 0critical: critical angle n: index of refraction |
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refraction of different waves at interface
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longer wavelengths (lower frequencies) move faster through a medium and therefore bend less at interface
shorter wavelengths (higher frequencies) move slower through medium and therefore bend more at interface |
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diffraction
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--- another type of wave-bending phenomenon
--- when wave moves through a small opening, it bends around the corners of that opening --- the smaller the opening and the larger the wavelength, the greater the diffraction --- smaller the hole the greater the spreading of light --- results in an image of light and dark bands or in dispersion and the creation of colors (depend upon destructive and constructive interference) |
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virtual image
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does not actually exist outside the mind of the observer
no light rays emanate from virtual image if a sheet of white paper is placed at the position of a virtual image, no image will appear on the paper ex: reflection in a flat mirror, a mirage, image under water |
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real image
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exists separately from the observer
rays of light actually intersect and then emanate from the point of intersection to form a real image if a sheet of white paper is placed at the position of a real image, the image will appear on the paper |
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two types of mirrors
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1. convex
2. concave |
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two types of lenses
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1. diverging (concave), acts like convex mirror
2. converging (convex), acts like concave mirror (3Cs: a thiCk Center Converges light) |
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radius of curvature
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for small section of curve is radius of extended circle
smaller radius of curvature indicates a sharper curve |
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focal point
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where light from horizontal rays is reflected by concave mirrors (or refracted by converging lenses) to focus on a single point
varies with frequencies |
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focal length
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--- length of separation between mirror or lens and the focal point
--- it is related to radius of curvature fmirror = 1/2r fmirror( focal length) = 1/2 (radius of curvature( --- focal point for a lens (flens) is affected by the refractive indices of the lens and the medium that the lens is in --- flens is also affected by radii of curvature of both sides of the lens |
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lens maker's equation
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1/flens = [(n1/n2)-1][(1/r1)-(1/r2)]
when n1=n2, lens will not refract light |
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power
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measured in diopters, which has equivalent units of m^-1
the inverse of the focal length P = 1/f P: power f: focal length of lens |
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lateral magnification (m)
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ratio of size of image to size of object (compare heights)
equal to negative of ratio of distance of image and distance of object from mirror or lens negative sign indicates that if both distances are positive, than the image is inverted m = -(di/do) = (hi/ho) m(magnification) = di(distance of image) / do(distance of object) = hi(height of image) / ho(height of object) |
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thin lens equation
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for any mirror or lens, distance of image is related to focal length and distance of object
(1/f) = (1/do) + (1/di) focal length --- object distance --- image distance --- applies to mirrors as well --- all measurements are given positive or negative values based upon their position relative to the mirror or lens |
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1st rule of mirrors and lenses
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draw an eye where observer will stand, and label side: positive, real and inverted (PRI)
"I (eye) am positive that real is inverted" images on side opposite the eye, are: negative, virtual and upright (NVU) |
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2nd rule of mirrors and lenses
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front of mirror is side that I (eye) am on
back of lens is side that I (eye) am on (stand behind camera to view object) objects are always positive when they are in front of a lens or mirror and always negative when they are behind a lens or mirror |
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3rd rule of mirrors and lenses
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if object is in front:
convex mirrors and diverging lenses make negative, virtual and upright images (NVU) concave mirrors and converging lenses make positive, real and inverted images (PRI), except when object is within the focal distance, in which case, they make a negative, virtual and upright image (NVU) |
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concave mirror and converging lens
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f is always positive
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convex mirror and divergent lens
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f is always negative
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lateral magnification of a 2 lens system
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product of lateral magnification of each lens
M = m1m2 |
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Effective power of 2 lenses in contact with each other
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equal to sum of their individual powers
Peff = P1 + P2 |
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Electromagnetic radiation equations
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c = f (wavelength)
c(speed of light) = frequency * wavelength n = c/v n(refractive index) = (speed of light in vacuum) * v(speed of light in medium) E = hf E:(energy of one photon) = h(planck's constant * freq n1sin01 = n2sin02 n: refractive index |
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Mirrors and lenses equations
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fmirror = (1/2)r
(focal length of mirror) = 1/2 * (radius of curvature) P = 1/f power = 1/focal length (1/f) = (1/di) + (1/do) f: focal length --- distance (image and object) m = -(di/do) = hi/ho m(magnification) --- height (image and object) |