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165 Cards in this Set
- Front
- Back
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torque
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torque=(force)(lever arm)sinø=Ia
I=moment of inertia, a=angular acceleration CCW is positive, CW is negative |
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terminal velocity
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when frictional force balances weight of object (f-mg=ma=0), usually mg>f
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mechanical advantage of pulley
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MA=Force out/Force in
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efficiency of pulley
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Efficiency=Work out/Workin=(Fd out)/(Fd in)
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Young's modulus
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Y=(F/A)/(∆L/L)
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bulk modulus
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B=(∆P)/(∆V/V)
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shear modulus
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S=(F/A)/(x/h)
A=area of face moving through distance x with original height h |
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pressure (taking hydrostatic pressure into account)
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P = P atm+dgh
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Pascal's principle
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an external pressure applied to a confined fluid will be transmitted equally to all points within the fluid
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Archimedes' principle
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buoyant force=weight of displaced fluid=dVg
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surface tension
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y=F/d
ratio of surface force to the length d along which the force acts |
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viscosity
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resistance exerted by a fluid in motion in newtons seconds per square meter
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continuity equation
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Q=Av=A1v1=A2v2
(q is fluid flow) |
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Bernoulli's equation
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E(total)=P+(1/2)dv^2+dgh=constant
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critical velocity (above give turbulant flow)
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vc=nRe/pd
(n=viscosity, Re=constant, p=density, d=diameter of tube) |
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laminar flow
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fluid flows in continuous layers stacked one on another and moving with same velocity
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turbulent flow
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fluid particles fluctuate between these laminar ordered layers as the velocity of fluid increases (random, chaotic motion gives vortices)
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linear expansion of solids
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∆L=aLo∆T
(a=constant, Lo=original length, ∆T=change in temp.) |
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volumetric expansion of liquids
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∆V=ßVo∆T
(ß=constant, Vo=original volume, ∆T=change in temp.) |
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Charles's law
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V1/T1=V2/T2
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Boyle's law
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P1V1=P2V2
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conduction
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heat energy transfer in solids, heat energy transferred by collisions between rapidly moving molecules of hot region to slower molecules of cold region)
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convection
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heat energy transfer in liquids and gases, transfer of heat energy due to physical motion or flow of heated suubstance carrying heat to cooler regions
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radiation
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heat energy transfer in space (and vacuum) by EM waves emitted by rapidly vibrating, electrically charged particles
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1st Law of Thermodynamics
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∆U=Q-W (change in internal energy)
W is positive when work is done by the system, Q is positive when heat is added to the system (and negative for opposite) |
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entropy change in equilibrium
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∆S=∆Q/T
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position of oscillating object
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x=Acos(wt+ø)
(A=amplitude in meters, w is angular frequency, t is time, ø is phase angle from reference) |
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frequency
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f=1/T
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angular velocity
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w=2πf=2π/T
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period
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T=2π/w
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Hooke's law
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F=-kx
a=-(k/m)x |
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period/frequency/angular velocity of mass-spring system
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T=2πsqrt(m/k)
f=(1/2π)sqrt(k/m) w=sqrt(k/m) |
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period of a pendulum
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T=2πsqrt(L/g)
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restoring force of a pendulum
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F=mgsinø
(ø=angle between negative tension vector and weight vector) |
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Doppler-shifted frequency
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f2=f1(v±vo)/(v±vs)
(top is positive if observer is moving toward source, bottom is negative if source if moving toward observer) |
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sound level
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ß=10log(I/Io)
(I is sound intensity) |
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wavelength/frequency of stretched string
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has nodes at both ends
harmonics: l=2L, L, (2/3)L f=nv/2L (n=1,2,3...) |
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pipe with both ends open
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has antinodes at both ends
harmonics: l=2L, L, (2/3)L f=nv/2L (n=1,2,3...) |
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pipe with both ends closed
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has nodes at both ends
harmonics: 1=2L, L, (2/3)L f=nv/2L (n=1,2,3...) |
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pipe with one end open
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has a node and antinode
harmonics: 1=4L, 2L, L f=nv/4L (n=1,2,3...) |
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beats
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fbeat=f1-f2
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waves in increasing frequency
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radio, micro, IR, vis, UV, X-rays, gamma rays
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critical angle
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sinø=n2/n1
(total internal reflection occurs as the angle is equal or greater than the critical angle to the normal) |
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incident light on a prism
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violet light bends more than red light for separation (lower wavelength is bent the most)
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2 slit bright fringes
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dsinø=ml where m=0,1,2...
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2 slit dark fringes
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dsinø=(m+1/2)l where m=0,1,2...
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magnification
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m=-di/do=hi/ho
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spherical mirror rays (concave)
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parallel to mirror normal: reflect back through focal length
through focal length: parallel to normal through radius of curvature: that's all |
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spherical mirror rays (convex)
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parallel to normal: draw fake line toward focal point and reflection on other real side
through focal length: reflects back to real side radius of curvature to object: that's all |
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thin lenses
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same ray tracing as mirrors
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lens maker's equation
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1/f=(n-1)(1/R1-1/R2)
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potential related to work
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V=-W/q
(electrical potential becomes stored as a result of work W done against an electric field to move a positive test charge q from infinity to that point) |
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electric potential difference
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∆V=Vb-Va=-Wab/q
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electric potential from a charged particle
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V=kq/r
(for more than one charge, add the V's together at each point) |
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electric field from a charge
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E=kq/r^2 N/C (V/m)
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electric dipole potential
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V=kqdcosø/r^2
(q is the charge on the two ± charges, r is the distance to the middle of the line between the charges, d is the distance between the charges, ø is the angle made to the line between the charges with the line making the radius r) |
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voltage by electromotive force
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V=E-IR
(E is the voltage or potential difference in the battery without current flowing, IR is subtracted because of an internal resistance when current flows) |
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current in series, parallel
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series: Inet=I1=I2=I3=In
parallel: Inet=I1+I2+...+In |
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voltage in series, parallel
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series: Vnet=V1+V2+V3+...+Vn
parallel: Vnet=V1=V2=Vn |
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electric potential energy W in a capacitor
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W=(1/2)qV=(1/2)CV^2=(1/2)q^2/C
(V is potential difference across plates, q is charge on each plate) |
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capacitance, area, distance
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C is proportional to area/distance
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dielectric and capacitance
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C'=KC
(K is dielectric constant) |
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Kirchhoff, loop rule
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potential drops around a circuit must be equal to zero, if resistor is traversed in direction of current, then ∆V=-IR (opposite current is +), if batter is traversed in direction of voltage then ∆V=+V (-V in opposite direction)
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difference between AC and DC
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DC have continuous, constant voltage and AC has sinusoidal voltaage causing periodic changes in direction of current flow (AC is associated with a frequency)
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voltage in AC at any given time
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V=Vosinwt=Vosin(2πft)
(Vo is max voltage) |
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root mean square voltage
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V(AC)=Vrms=Vmax/sqrt(2)
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root mean square current
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I(AC)=Irms=Imax/sqrt(2)
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AC relation between current and voltage
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Vrms=IrmsR
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inductance
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impedes voltage and caused by reversed emf induced by changing magnetic fields as voltage rises and falls
Vrms=IrmsX(L) X(L)=inductive reactance, represents ability of inductor to resist flow of AC current X(L)=2πfL=wL L=inductance loop of circuitry is an inductor |
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pure capacitance
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for AC circuit with capacitor:
Vrms=IrmsX(C) X(C) is capacitive reactance X(C)=1/(2πfC) |
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resistance, inductance, and capacitance in combination
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Z=sqrt(R^2+(X(L)-X(C))^2)
Vrms=IrmsZ |
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phase angle in AC
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angle between voltage and current
tanø=(X(L)-X(C))/R |
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power dissipated in AC circuit (average power)
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Pavg=(Irms)(Vrms)(cosø)
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magnetic field of long straight wire
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B=µI/(2πr), r is distance to wire axis
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magnetic field at center of circular coil
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B=µNI/(2r), r is radius, N is number of number of loops of coil
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magnetic force on a charged particle in motion
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F=qvBsinø
(ø between B field and velocity, right hand rule: thumb=v, fingers=B, palm=F) |
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magnetic force on a current-carrying wire
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F=ILBsinø
(L=length of wire, ø=angle b/w current and B field, right hand rule: thumb=I, fingers=B, palm=F) |
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photoelectric effect
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KEmax = hv-Wmin
(maximum kinetic energy of electron being released from atom by light greater than its work function, the minimum amount of work required for electron liberation) |
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energy level of an electron
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E=-(13.6 eV)(Z^2/n^2), as n increases the energy differences become smaller
(Z=atomic number, n=shell) |
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radioactive decay
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N(t)=No e^(-lt)
l (lamba)=ln(2)/T(1/2) |
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alpha decay
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caused by repulsive electric forces between protons
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beta decay
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nuclei with too many neutrons emit beta particle (B- is an electron (Z up 1, A unchanged), B+ is a positron (Z down 1, A unchanged)
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rest mass of nucleus and mass defect
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less than the sum of the rest masses of the protons and neutron, negative energy (gives off energy) required to bind individual nucleus particles
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nuclear binding energy
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NBE=Zm(p)c^2+Nm(n)c^2-M(nuc)c^2
(mass defect is M(nuc)c^2) |
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nuclear fission and fusion
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fision usually occurs when A>230 and fusion when A<20
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pressure units
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1 Pa = 1 N/m^2
1 atm = 1.01 x 10^5 Pa = 1.01 bar = 760 mmHg = 760 torr |
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5 motion equations
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1. Vf=Vo+at
2. x=.5at^2+Vot+Xo 3. Vf^2=Vo^2+2as 4. Vavg=(Vf+Vo)/2 5. s=Vavg x time |
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Newton's 3 laws
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1. inertia (remain at rest or constant V unless force)
2. F=ma 3. Fa=-Fb |
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uniform motion
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when object speed remains constant (in centripetal, only radial acceleration)
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nonuniform motion
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speed of object changes, so there is some tangential and some centripetal circular accerlation
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work
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Fdcosø
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total mechanical energy
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E=KE+PE
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work-energy theorem
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W=∆KE
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conservative forces
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work done to move particle in round trip is zero, work to move particle between 2 points is the same regardless of path (any force with associated PE, ∆E=∆KE+∆PE=0)
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nonconservative force work
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W'=∆KE+∆PE=∆E
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conservation of angular momentum
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L=mvr where as r increases v decreases so that L remains constant
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conduction
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direct transfer of energy from molecule to molecule by collisions (metals are best, gases are worst)
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convection
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transfer of heat by physical motion of heated material (fluids), heated parts rise and colder parts sink
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special cases of first law of thermodynamics
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adiabatic (∆U=-W), constant volume (∆U=Q), closed cycle (Q=W)
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entropy of system in reversible isothermal process
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∆S=Q/T
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conservations in hydraulic lever
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∆P=F1/A1=F2/A2
Volume=A1d1=A2d2 Work=F1d1=F2d2 |
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float or sink?
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if fluid displaced by object has a greater weight than object then the object will float, it will sink if fluid weight is less than object weight until the two are balanced
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streamlines
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velocity is tangent to line and lines may not cross
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liquid/gas viscosity
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in fluids, liquid has greater viscosity than gas
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electric field and force
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E=F/q, F=Eq
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heat equations
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q=mL and q=mc∆T
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E field lines
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point away from positive charge and into negative charge, E at any point is tangent to the line, total E is equal to the vector sum at any point from a number of charges
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potential from a number of point charges
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add up the V=kq/r from each charge (scalar sum)
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equipotential line
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every point along line has equal potential, no work done in moving charge along these lines
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work to move charge to new potential
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Wab=q(Vb-Va)=q(kQ/rb-kQ/ra)
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object falling with friction
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Ff-mg=ma (terminal velocity when Ff=mg)
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electric potential energy
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EPE=W=qV=kqQ/r (work needed to move charge from infinity to that point)
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dipole moment
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p=qd, points from negative to positive charge
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electric field along perpendicular bisector of electric dipole
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E=(1/4πEo)(p/r^3), points in opposite direction of p
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dipole in electric field
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generally random orientation without field, zero translational force in field because the force on each charge is equal in magnitude and opposite in direction, there is nonzero torque to align dipole moment with E field (torque=pEsinø) with ø the angle between dipole and E
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torque on dipole in E field
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torque=pEsinø (ø is angle between dipole and E)
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circular motion of charged particle
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F=qvB=mv^2/r, r=mv/qB
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diamagnetic
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individual atoms have no net magnetic field, repelled from strong bar magnet, weakly antimagnetic
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paramagnetic
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individual atoms have a net magnetic field but they are aligned randomly so whole material has no magnetic field, some degree of alignment occurs and be attracted towards pole of strong bar magnet (weakly magnetic)
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ferromagnetic
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individual atoms have net magnetic field bu randomly aligned as in paramagnetic, temp below a critical value causes a high amount of alignment and atomic B field occurs (above critical value the material is paramagnetic, otherwise strongly magnetic and if the critical temperature is greater than room temp then you have a bar magnet)
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insulators
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have electric charge bound to constituent atoms to retard electron flow (nonmetals)
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power dissipated by resistor
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P=IV=I^2R=V^2/R
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total resistance for n equal resistors in parallel
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Rtotal=R/n
(R is resistance of each) |
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capacitance
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C=Q/V=EoA/d
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electric field between capacitor plates
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E=V/d (toward negative plate away from positive plate)
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function of dialectric
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lowers voltage across charged up capacitor and makes room for more charge to increase capacitance (charge remains the same before and after)
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AC current equation
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I=Imaxsin(2πft)=Imaxsin(wt)
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linear restoring force of simple harmonic motion (spring)
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F=-kx and a=(-w^2)x
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energy in SHM
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E=K+U=constant
K=.5mv^2 U=.5kx^2 (spring) =mgh (pend.) (at equilibrium position KE is max and PE is zero, at max displacement PE is max and KE is zero) |
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transverse wave
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particle oscillates perpendicular to direction of wave motion
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longitudinal wave
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particle oscillates in direction of motion
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traveling wave
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string fixed at one end, incident wave is reflected and inverted back
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standing wave
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ends are either nodes or antinodes as in strings and pipes, there is no energy propagation
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resonance
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when forced oscillation occurs at natural frequency, energy is inputted and amplitude increases
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sound
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longitudinal wave, moved by mechanical disturbance propagated through deformable medium (sound is fasted in solid then liquid then gas)
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power-intensity
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Power=Intensity x Area
(intensity is avg. rate per unit area at which energy is transported across a perpendicular surface by the wave) |
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ratio of sound levels
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Ba-Bb=10log(Ia/Ib)
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sound production
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1. vibration of solid object that sets adjacent air molecules in motion
2. acoustic sound (vibrating motion of air) 3. pitch determined by length of pipe on tension in string |
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beat frequency
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fbeat=f1-f2 (wavelengths add)
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plane mirrors
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virtual images, law of reflection (angles equal)
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focal length sign conventions
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converging lenses/mirrors have positive focal lengths, diverging lenses/mirrors have negative focal lengths
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lens power
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P=1/f(meters) in diopters
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lenses in contact (f, P, M)
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1/ftot=1/f1+1/f2+...
P=P1+P2+... M=m1 x m2 x m3 x ... |
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index of refraction function
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increasing n causes decrease in lamba, decrease in velocity and no change in frequency (n=lamba in vacuum/new lamba)
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dispersion
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separation of wavelengths as different wavelenghts of light have different speeds when frequency remains constant (causes violet light to bend more as it moves slower)
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blackbody spectrum
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lamba(peak)=2.9x10^-3mK/T
E=sigmaT^4 (energy emitted per unit area per second) (blackbodies at higher temp have lower peak lamba) |
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ionization energy and work function
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KE (ionization) = hf (photon) - w (work function of a threshold photon energy for ionization)
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current produced from light beam
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current created by shooting light at metal with high enough energy, higher intensity causes greater current (directly proportional) (frequency of light must be greater than threshold frequency)
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fluorescence
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substances emit visible light when excited by other radiation (usually UV), the electron returns to its state in 2 or more steps and at each step a longer wavelength is emitted
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electron capture
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unstable radionuclei can capture K or L shell electron as it combines with a proton to form a neutron (Z decreases by 1, A stays the same)
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iron peak
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binding energy per nucleon peaks at iron (most stable nucleus)
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decay equation
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N=Noe^(-lt) and l=(ln2)/T(1/2)
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general gravitational potential energy (not local, mgh)
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PE=-GmM/r
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wave amplitude and intensity
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amplitude is directly related to the intensity of the wave
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sound attenuation
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conversion of sound wave energy into heat
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sound pitch
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the frequency of the sound, higher pitches have higher frequencies
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acoustic resonance
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the tendency of an acoustic system to absorb energy if frequency of oscillations matches natural frequency
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ultrasound
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20 kilohertz or greater (humans can't hear)
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electrostatic induction
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an electrically charged object can charge an uncharged object even without direct contact between the two
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solenoid
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coil is wrapped around central object where current flows through the coil to generate a magnetic field of center object (B=uNI constant in interior, N is loops of coil per meter)
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toroid
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magnetic circular solid core with wire wrapped around with current flowing, magnetic field in center of circle is B=uNI/2πr (N loops)
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thin film interference
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light waves can be reflected on top of film or at the bottom and can interfere constructively if the n of the film is greater than the underlying substance and destructively if the n is less than the underlying (phase shifts 180 and interferes with first reflected wave)
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diffraction grating
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lines situated close together can diffract light into constituent wavelengths (dispersion)
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single slit diffraction
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largest bright fringe iin center, dark fringes found by sinø=ml/d (l=lambda, d=slit width, m=1,2,3...)
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x-ray diffraction
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scattering of light through specimens based on thickness and material of specimen
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