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150 Cards in this Set
- Front
- Back
Missing "a" (missing acceleration)
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d = (1/2) (v0 + vf) t
("d" equals the average of the "v's" times "t") |
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Missing "d" (missing displacement)
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vf = v0 + at
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Missing "vf" (missing velocity final)
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d = v0*t + (1/2)at^2
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Missing "v0" (missing initial velocity)
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d = vf*t - (1/2)at^2
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Missing "t" (missing time)
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vf^2 = v0^2 + 2ad
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Info about "Scientific Reasoning: The Physical Sciences" (1)
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- 52 q's, 70 minutes
- 4 to 7 mult choice questions after each passage - some MC not related to passages - scored from 0 to 15 |
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Info about "Verbal Reasoning" (2)
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- 40 questions, 60 minutes
- similar to reading comprehension of other standardized exams - tests ability to paraphrase passages, draw inferences, characterize themes, and follow lines of reasoning from the passage |
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Info about "Writing Sample" (3)
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- 2 essays, 30 min each
- comment on a philosophy or point of view |
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Info about "Scientific Reasoning: The Biological Sciences" (4)
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- 52 q's, 70 min
- biology and organic chemistry - same structure as physical sciences |
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slope (m) = ?
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(y1-y2) / (x1-x2) = Δy / Δx
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how to convert between degrees and radians in angles?
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use this conversion factor:
180 degrees = π radians |
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Pythagorean theorem:
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a^2 + b^2 = c^2
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SOH-CAH-TOA
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sinx = opp/ hyp
cosx= adj / hyp tanx = opp / adj = sinx / cosx |
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30-60-90 right triangle: what is the ratio of the sides (from smallest leg to hypotenuse)?
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1 : sqrt(3) : 2
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45-45-90 right triangle: what is the ratio of the sides (from smallest leg to hypotenuse)?
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1 : 1 : sqrt(2)
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3:4:5 triangle
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this is a special ratio of side lengths of specific right triangles
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Def: displacement
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a vector quantity describing the "net change in position" (from start to end)
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average velocity = v-bar = ?
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displacement / change in time =
d / Δt |
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average speed = ?
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total distance / change in time
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average acceleration = a-bar = ?
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change in velocity / change in time =
Δv / Δt = (vf - vi) / Δt |
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If velocity and acceleration are pointing in the same direction, the object is "________ _____"
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speeding up
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If velocity and acceleration are pointing in opposite directions, the object is "________ _____"
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slowing down (still could be moving in the direction opposite of acceleration)
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If velocity and acceleration are pointing perpendicularly to eachother, the object is "__________ ______"
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changing direction
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Velocity vs. Time graphs: what does the slope represent?
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acceleration
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Velocity vs. Time graphs: what does the area under the curve represent?
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displacement
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Velocity vs. Time graphs:
when does a change in direction of the object occur? |
when the graph crosses the horizontal axis
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Velocity vs. Time graphs:
what does area under the horizontal axis represent? |
negative displacement
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Kinematics proportion (from vf=v0 + at)
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vf is directly proportional to t
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Kinematics proportion (from d = v0t + 1/2at^2
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d is directly proportional to t^2
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Kinematics proportion (from vf^2=v0^2 + 2ad)
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vf^2 is directly proportional to d
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When an object is thrown upward, it ____ ______ by approximately 10 m/s every second
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slows down
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When an object falls downward, it ____ ______ by approximately 10 m/s every second
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speeds up
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Solving projectile motion problems:
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- separate x and y equations
- v_x = d_x/t is the only equation needed for the x equations - time is the bridge between the two equation sets |
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Def: centripetal acceleration
a_c = ? |
- acceleration directed toward the center of the circle
- a_c=v^2/r - a_c is directly proportional to v^2 |
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formula for period of a circular revolution (time it takes to go around circle once)
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T = 2πr / v
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What's a simple definition of force?
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a "push" or a "pull"
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Newton's First Law:
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"A body--in motion or at rest--will remain in its initial state unless acted upon by a nonzero net external force."
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What is inertia?
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the natural tendency of objects not to accelerate.
- mass is a measure of inertia |
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Newton's Second Law:
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F_net= m*a
(a net external force will produce acceleration) Force is directly proportional to mass |
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What are the units of force?
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Newtons (N)
- 1 N = 1 kg * m/s^2 |
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Net force
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the vector sum of all forces acting on an object
- F_net = F_1 + F_2 + ... - split forces into x and y components when necessary |
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Newton's Third Law:
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"when one body exerts a force on another, the second body will exert an equal and opposite force on the first" (think of normal force)
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Formula for force of gravity for objects near earth's surface (aka "weight")
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F_g = m * g
m = mass g = 10 m/s^2 |
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Newton's Law of Universal Gravitation:
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F_g = (G * m_1 * m_2) / r^2
- F_g is directly proportional to mass of each object - F_g is inversely proportional to the square of the distance between the centers of the two objects (r) |
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What is "normal force"
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force exerted by a surface perpendicularly to the surface
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___________ is always a pulling force on the MCAT.
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Tension
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The 2 types of Friction and their notation:
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- Kinetic Friction (sliding) = F_f,k'
- Static Friction (not sliding) = F_f,s' |
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Equation for Kinetic Friction
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F_f,k' = μ_k * F_N
μ_k = coefficient of kinetic friction F_N = normal force |
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Inequality for Static Friction
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F_f,s' ≤ μ_s * F_N
μ_s = coefficient of static friction F_N = normal force - μ_s * F_N is the maximum value for force of static friction before an object begins to move - static friction equals the magnitude of the applied force |
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Centripetal force equation
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F_c = m*a_c = m * v^2/r
- centripetal force is not a new force, but a general term for any centerseeking force like gravity or tension |
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center of mass equation
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x_cm = (m_1*x_1 + m_2*x_2 + m_3*x_3 + .....) / (m1 + m2 + m3 + ...)
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What is "rotational inertia" or "moment of inertia" (hint: related to rotational motion)
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the property that makes rotational acceleration difficult
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Info about Moment of Inertia
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- denoted by "I"
- measured in kg * m^2 - increases with mass - increases with how far away the mass is from the axis of rotation (think of figure skater with arms out and with arms in while spinning) |
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Torque (definition)
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- torque is created by a force that produces rotation
- required for rotational acceleration to occur just like force is required for translational acceleration to occur - denoted by "τ"; measured in N * m |
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Torque (equation)
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τ = r*F*sinθ
τ = torque r = distance from pivot to point of applied force F = applied force θ = angle between r and F |
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Torque (equation with lever arm)
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τ = L * F
τ = torque L = lever arm = shortest distance from pivot to line of action (line of action is the line of the force) F = applied force magnitude |
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Statics: Translational equilibrium
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When no net force is acting on an object (object is still)
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Statics: Rotational equilibrium
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When no net torque is acting on a body (object is not rotating)
- set counterclockwise (CCW) torques equal to clockwise (CW) torques in rotational equilibrium |
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sin (60 degrees)
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sqrt(3) / 2 = 0.87
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cos (45 degrees) and sin(45 degrees)
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sqrt(2) / 2 = 0.71
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sin(30 degrees)
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1/2 = 0.5
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Definition and Formula for Work (units as well)
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- Work is a measure of how much a force succeeds in moving an object in the direction of the displacement
- W = F*d*cosθ where d = displacement and Fcosθ = the component of the force in line with the displacement - measured in Joules (N*m); work is a scalar |
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The Signs of Work
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- Work is positive when cosθ is positive;
- work is neg when cosθ is neg (between 90 degrees and 180 degrees) - work is 0 when cosθ = 0 (which means θ= 90) |
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Total Work formula
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W_total = W_1 + W_2 + W_3...
total work is a scalar sum |
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Work done by Changing Forces
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- if force is not constant, then the formula for work (W=Fdcosθ) cannot be used
- Calculate the area under the curve in a Force (N) vs. Position (m) graph |
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Work done by Gravity
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- the work done by gravity is independent from it's path since gravity is a conservative force
- the vertical displacement is "d" - use the formula W_g = mgΔh |
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Kinetic Energy Formula
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KE = (1/2) mv^2
- measured in Joules (N*m) |
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Work-Kinetic Energy Theorem
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W_total = ΔKE = KE_f - KE_0
- if a force does positive work, there is an increase in KE - if a force does negative work, there is a decrease in KE |
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Gravitational Potential Energy
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PE_g = mgh
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Work due to Gravity
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- the Work due to gravity can be seen as:
W_g = -ΔPE |
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Law of Conservation of Energy
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"The energy of an isolated system remains constant"
- in such a system, energy can neither be created or destroyed, only converted to different forms |
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Mechanical Energy Equation
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E = KE + PE
KE = kinetic energy PE = potential energy |
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Law of Conservation of Mechanical Energy
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E_0 = E_f
KE_0 + PE_0 = KE_f + PE_f |
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Nonconservative forces and Conservation of Energy
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- there are 3 conservative forces: gravity, electrostatic force, and spring force
- If F is a nonconservative force (like friction or all applied forces), then: KE_0 + PE_0 + W_F = KE_f + PE_f |
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Mechanical Advantage
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applied force (F) is inversely proportional to displacement (d) according to W=F*d*cos(theta)
- simple machines like pulleys, levers, and inclined planes create mechanical advantage by **reducing required applied force and increasing displacement** |
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Power formula and units
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- power is the quantity of work performed over time
- Power = W / ΔT - measured in Watts (W) = 1 J/s |
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Alternate formula for Power
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P = F*v*cosθ where v = velocity and F*cosθ = component of F that is pointing in the direction of the velocity
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Linear momentum (p)
- Formula - Units - Vector or scalar? |
p = m*v
m = mass v = velocity - Units: kg*m/s - p is a vector since v (velocity) is a vector |
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Impulse (J)
- Definition - 2 formulas - proportion |
- Impulse: the change in momentum
- Formula #1: J = Δp = p_f - p_0 - Formula #2: J = F_avg * Δt - Proportion: F_avg is inversely proportional to Δt |
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In which type of graph does the area under the curve correspond to impulse?
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in a Force (N) vs. time (s) graph
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Conservation of Linear Momentum Definition and Equation
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"If 2 objects hit eachother without any other external forces, total momentum of the system is conserved"
P_A0 + P_B0 = P_Af + P_Bf |
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Elastic Collisions
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In elastic collisions and inelastic collisions, momentum is conserved. However, in elastic collisions, KE is also conserved
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Inelastic Collisions
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In elastic collisions and inelastic collisions, momentum is conserved. However, in inelastic collisions, KE is NOT conserved.
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Perfectly Inelastic Collisions
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When during a collision, the KE is not conserved and the objects stick together and move together after collision
- combine masses when finding the final momentum: (m_1 + m_2) * v_f |
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Collisions in Two Dimensions
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since momentum is a vector, the components of momentum are also conserved during a collision
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Recoil or Explosion and Conservation of Momentum
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Total momentum is also conserved when two objects begin as one and then separate (verb) from each other
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How are solids different than liquids?
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Solids don't flow
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Density (ρ)
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Density = Mass / Volume (in kg/m^3)
- density is a conversion factor to/from volume from/to mass |
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Specific Gravity
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S.G. = ρ_fluid / ρ_water
* ρ_water = 1000 kg/m^3 * S.G. is unitless since its a ratio of densities |
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What are the two characteristics of tensile stress?
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- tensile stress refers to a force that is equally applied to both ends of a solid
- tensile stress refers to a force that tends to compress or stretch a solid |
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What is the equation for Tensile Stress (T_ss)?
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T_ss = F / A_c
A_c = cross sectional area F = applied force - units = N/m^2 = 1 Pascal = Pa |
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Define Tensile Strain:
What's the equation for Tensile Strain (T_sn)? |
Tensile Strain refers to the degree that tensile stress changes the length of an object
- T_sn = ΔL / L_0 * ΔL = change in length * L_0 = initial length - T_sn is unitless since it's a ratio of lengths |
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What is Young's modulus a ratio of?
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YM = T_ss / T_sn
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Density of liquids and density of gases
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- density of liquids is fairly constant
- density of a gas will change at varying temperatures and pressures |
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Formula for pressure:
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Pressure = Force / Area (units: N/m^2 = 1 Pascal)
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Fluid pressure definition
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- Fluid pressure is the pressure exerted by a fluid on a real or hypothetical body
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What is the formula for gauge pressure (a type of fluid pressure)?
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P = ρ*g*h
- gauge pressure does not include atmospheric pressure - ρ = density of fluid - g = 10 m/s^2 - h = height of fluid above a specific point |
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What is equation for absolute pressure?
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Absolute pressure = gauge pressure + atmospheric pressure
= ρgh + atmospheric pressure |
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Pascal's principle:
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- "pressure exerted on an enclosed fluid it equally transmitted to every part of the fluid and also on the walls of the container"
- "fluid pressure at any given depth in a resting fluid is unrelated to the shape of the fluid's container" |
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Proportions in the fluid pressure equations (P = ρgh)
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P is directly proportional to ρ (density) and to h (depth)
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Define buoyancy:
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Buoyancy refers to a fluid's tendency to propel submerged or partially submerged objects up towards the surface
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Description and Equation of Bouyant Force (Archemides' Principle):
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- the buoyancy force is an upward force exerted by a fluid on another body or fluid.
- Buoyancy (F_b) = V * ρ * g = weight of displaced fluid * V = volume of displace fluid * ρ = density of fluid * g = acceleration due to gravity (10 m/s^2) |
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Flow (Q): description and equation
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the volume of fluid that passes a given point in a given period of time
- Flow (Q) = A*v (A = cross sectional area of pipe; v = velocity of pipe; units = m^3/sec |
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Characteristics of Ideal Flow
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1) flow is constant at all points
2) ideal flow has no viscosity 3) Ideal flow has no turbulence 4) ideal flow has no fluid friction (drag) 5) flow = velocity * area |
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The Bernoulli Equation: description and implications
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Bernoulli's equation implies that at high velocities, fluid pressure decreases, and at low velocity, fluid pressure increases
- v = sqrt(2gh) |
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Laminar flow
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smooth flow of liquid in layers with no whirpools
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Turbulent flow
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flow that contains whirpools and eddies
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Fluids flowing through a pipe with changing caliber: proportions
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velocity is inversely proportional to cross-sectional area
pressure increases with cross-sectional area |
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What are qualities of conductors?
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- they are usually metals
- they have high electron mobility |
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What are qualities of insulators
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- low electron mobility
- nonmetals like rubber and glass |
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What is Coulomb's Law?
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F_e = k * q_1 * q_2
-------------------- r^2 where k = 9*10^9 = 1/(4πε_0) |
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What is Electric Field Strength (E)?
What direction does Electric Field point in? What are the units of Electric Field? |
- the hypothetical force on a +1 charge at a specific distance
- electric field extends from a charge in all directions and points in the direction a test charge would move in - Units: N/C |
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Describe a capacitor:
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- two closely spaced plates parallel to each other with equal area
- each plate has equal and opposite charge |
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What's the formula for Electric Field within a Capacitor?:
Proportions? |
E=Q/(ε_0 * A)
(units: N/C) Electric field is proportional to charge and inversely proportional to area |
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What is the definition of Electrostatic potential of a capacitor?
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Electrostatic potential refers to the potential energy possessed by a massless particle with |q| = 1 situated on the like-charged plate of the capacitor
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What is the equation for Electrostatic Potential of a Capacitor?
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V = E*d
V = electrostatic potential (J/C) E = electric field strength (N/C) d = distance between capacitor's plates |
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How is Electrostatic Potential within a Capacitor similar to Gravitational Potential energy/Work?
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in the formula V=Ed, E represents the force repelling the test charge, d represents the "height" the charge will move, and V represents the "gravitational potential energy"
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What is capacitance (definition)?
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Capacitance is the ability of a capacitor to store electric charge.
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What 2 things is Capacitance (C) proportional to?
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Capacitance is proportional to (Q/V)
Capacitance is also proportional to Area of the plate |
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What is the equation of capacitance and what are its inherent proportions?
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C = (k * ε_0 * A) / d
k= dielectric constant A = area of capacitor's plates d = distance between plates - C is directly proportional to Area and inversely proportional to distance btw plates |
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Explain what dielectric breaking point is.
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At high values of Electric Field (E), stored charge in a capacitor will be discharged. This E value corresponds to the dielectric's "breaking point."
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How is electromotive force (emf) produced in a circuit?
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by the difference in electric potential at each terminal
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From which terminal of the voltage source do electrons flow in a circuit?
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Electrons flow from the negative terminal to the positive terminal
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What is the definition of current in a circuit?
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Current is the flow of positive charge; current flows from the positive terminal of the battery in a circuit
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What is the definition of voltage in a circuit?
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Voltage is the difference in elec. potential btw the cathode and the anode measured in Volts
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What is Ohm's Law for circuits? What are it's inherent proportions and other algebraic forms?
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V = IR
(V = voltage (Volts); I = current (A); R = resistance (Ω - ohms) |
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What is the formula for Power in a circuit?
When combining this formula with Ohm's Law, what other versions of the formula exist? |
P = I*V
P = I^2 * R P = V^2/R |
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What are resistors?
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Objects that conduct electricity poorly (like lightbulbs)
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What is the formula for total resistance when resistors are connected in series?
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R_total = R_1 + R_2 + R_3...
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What is the formula for total resistance when resistors are connected in parallel?
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1/R_total = 1/R_1 + 1/R_2 + 1/R_3...
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What formula should you use to calculate voltage drop at each resistor in a circuit?
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V = IR (Ohm's Law)
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How are magnetic fields produced? What direction does the vector (magnetic field) have at all points in a circular path?
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By flowing electrons; when magnetic field is rotating around a wire, the magnetic field points as a vector tangential to the circle.
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How does magnetic field strength around a wire change when distance from the wire changes?
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Magnetic field strength is greater near the wire and less from the wire.
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What is the symbol and unit for magnetic field strength?
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B; in Teslas
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How do you determine the direction of magnetic field (B) around a wire?
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Use the right hand rule where your thumb points in the direction of the current (flow of positive charge) and your fingers curve in the direction of magnetic field.
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How do you determine the direction and magnitude of the force produced by a magnetic field?
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- to determine direction of the force, put your right hand flat and point fingers in direction of field (B), thumb in direction of velocity (v), and then the palm will point in the direction of force (F) on a positive charge.
- magnitude of force: F = q*v*B |
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In the context of transverse waves, what do cycle, period, wavelength, amplitude, and frequency mean?
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Cycle = one crest and one trough
Period (T)= time for one cycle to occur Wavelength (λ) = distance traveled by one cycle Amplitude (A) = height from middle line of a wave and crest of the wave Frequency (f)= amount of cycles per second |
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How are period and frequency related in the context of transverse waves?
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F = 1/T
T = 1/f T = period in seconds/cycle f = frequency in cycles/second (aka Hertz (Hz)) |
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How are velocity of a wave, frequency and wavelength related in the context of waves?
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v = f * λ
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In longitudinal compressional waves, what parts of the waves are analogous to crest and troughs?
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crest = compression
trough = rarefraction |
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How do density of a medium and resistance to compression affect the speed of sound?
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The speed of sound decreases when the density of a medium increases;
- the speed of sound increases when resistance to compression increases |
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How are loudness (β) and Intensity (I) of sound related? What are the units of loudness (β) and intensity (I)?
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β = 10 * log (I / I_0)
β = loudness (in decibels) I = intensity of the sound (W/m^2) I_0 = lowest intensity that is dectectable by humans (10^-12 W/m^2) - when intensity is multiplied by 10^x, β increases by 10(x) |
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In an oscillating spring or pendulum, where is the point of highest velocity?
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At the point when the spring/pendulum is in it's relaxed position
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In an oscillating spring, what happens to the kinetic energy and potential energy of the spring?
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Kinetic energy and potential energy are converting into eachother back and forth.
mgh_max = 1/2mv^2_max |
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What is Hooke's law in the context of springs?
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F = - k * x where k is the spring constant and x is the displacement from the relaxed position
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How can one approximate the spring constant of a pendulum
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k for pendulums ≈ wt of pendulum / length of pendulum
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Is the total energy of a oscillating system constant or changing?
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Total energy is constant in a oscillating system (spring or pendulum)
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What is the range of sound frequencies that are detectable by human ears?
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10 Hz - 20,000 Hz
- sound below the lower threshold is called infrasonic - sound above the top threshold is called ultrasonic |
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Describe the Doppler Effect in the context of sound and pitch:
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As the source of sound approaches an observer, the pitch (apparent frequency) increases and then suddenly decreases once the source begins to move away from the observer.
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What is the equation for Doppler effect?
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f_0 = f_s [(v ± v_0)/(v ± v_s)]
f_0 = apparent pitch (not true frequency) f_s = frequency of source's sound v = velocity of sound in that medium v_0 = velocity of the observer v_s = velocity of the source Note: assign positive and negative by this rule - if the observer is moving towards the source, then the fraction would need to get bigger so numerator's sign would be positive; if the source is moving towards the observer, then the fraction would need to bigger so the denominator's sign would be smaller. |