physics constants and equations

Question 1

kinematic equations

Answer 1

1. V=V_o+at
2. Δx=V_ot+1/2at²
3. V²=V_o²+2a(Δx)

Question 2

Gravitational force btwn 2 objects

Answer 2

F=(Gm₁m₂)/r²

Question 3

gravitational constant

Answer 3

6.67x10^-11 N x m²/kg²

Question 4

torque

Answer 4

t=rFsin(Θ)

Question 5

centripetal foce

Answer 5

F=(mv²)/r

Question 6

centripetal acceleration

Answer 6

a=V²/r

Question 7

friction force

Answer 7

coefficient of static or kinetic friction times normal force

Question 8

Kinetic energy

Answer 8

K=1/2mv²

Question 9

Potential energy

Answer 9

U=mgh

Question 10

Relating work to energy

Answer 10

W=ΔE=ΔK+ΔU

Question 11

work

Answer 11

W=Fd cos Θ

Question 12

power

Answer 12

P=w/t

Question 13

net work

Answer 13

W=ΔK

Question 14

momentum

Answer 14

p=mv

Question 15

impulse

Answer 15

change in momentum

I= Δp (momentum) = FΔt = mv_f-mv_i

Question 16

difference between elastic and inelastic collisions

Answer 16

kinetic energy is only conserved for elastic collisions

momentum is conserved for both

Question 17

mechanical advantage

Answer 17

F_out/F_in

Question 18

Efficiency

Answer 18

W_out/W_in=[(load)(load distance)]/[(effort)(effort distance)]

effort and load in Newtons

Question 19

center of mass

Answer 19

(m₁x₁ + m₂x₂ +…)/ m1 + m2 + …

Question 20

Thermal expansion (ΔL)

Answer 20

ΔL = αLΔT

L is length, T is temp, alpha is a constant

Question 21

volume expansion

Answer 21

liquids experience thermal expansion –volume expansion

ΔV=βVΔT

β=3α

Question 22

change in the internal energy

equation and sign convention

Answer 22

ΔU = Q - W

Q is energy transfered through heat to system and W is work done by system.

Work done on the system (-) / work done by system (+)

heat flow out of system (-) / heat flow into system (+)

Question 23

conversion between Cal, cal, Btu, and Joules

Answer 23

1 Cal = 1000 cal = 3.94 Btu = 4184 J

Question 24

equation used to find heat gained or lost by a substance subjected to a change in temperature

Answer 24

Q=mcΔt

Question 25

equation used to determine heat gained or lost by a substance when tehre is a change of phase

Answer 25

Q=mL m is mass L is heat of transformation Q is heat gained or lost

Question 26

Work done on or by a system that undergoes a change in volume at constant pressure

Answer 26

W=PΔV

Question 27

entropy

Answer 27

ΔS=Q/T

Question 28

entropy for a reversible process

Answer 28

ΔS=Q/T=L(m/T) L = latent heat (either heat of fusion or heat of vaporization)

Question 29

density

Answer 29

p=m/V

Question 30

Work in terms of density

Answer 30

W=pVg derivation: W=mg m=pV W=mVg

Question 31

Pressure

Answer 31

Pressure = F/A

Question 32

conversion between Pa, atm, torr, mm Hg

Answer 32

1.013 x 10⁵ = 1atm = 760 torr = 760 Hg

Question 33

Absolute pressure

Answer 33

the total pressure exerted on an object submerged in a fluid P=P_o+pgh P_o is pressure at the surface pgh(density,gravity,height)

Question 34

guage pressure

Answer 34

the difference between absolute pressure inside and atmospheric pressure outside P_g=P-P_atm = (P_o + pgh) - P_atm

Question 35

pascals principle

Answer 35

P = F1/A1 = F2/A2 V=A₁/d₁=A₂/d₂ d is liquid displaced W=PΔV so W=F₁d₁ = F₂d₂

Question 36

buoyant force (for floating objects and for fully submerged objects)

Answer 36

F_buoy= (V_{fluid displaced})(p_fluid)(g) = weight of object for fully submerged objects, F_buoy=(V_{object submerged})(p_fluid)(g)

Question 37

ciritical viscosity

Answer 37

critical velocity is the velocity at which, when exceeded, flow of fluid becomes turbulent V_c=N_Rn/pD N_R is reynolds number, n is viscosity of the fluid, p is density of fluid and D is diameter of tube

Question 38

Linear velocity at which fluid flows

Answer 38

measure of linear displacement of a fluid particle in a given amount of time vA=V/time v is velocity V is volume

Question 39

continuity equation

Answer 39

fluids flow more quickly through narrow passages than wide ones v₁A₁ = v₂A₂ = constant v is velocity

Question 40

bernoulli's equation

Answer 40

P₁ + (ρv_1² )/2+ ρgy₁ = P₂ + (ρv₂²)/2+ ρgy₂

Question 41

Young's modulus

Answer 41

change of length due to stretching or pushing forc;e Y=(F/A) / (ΔL/L)

Question 42

shear modulus

Answer 42

S = (F/A)/(x/h)

Question 43

Bulk modulus

Answer 43

degree to which a material will experience a change in volume in relation to applied pressure (gasses mostly) B = (F/A) / (ΔV/ V)

Question 44

what is the fundamental unit of charge

Answer 44

e=1.6 x 10^-19

Question 45

coulombs law

Answer 45

F=(kq₁q₂)/(r²) constant electric field: F=Eq

Question 46

what does K (coulombs constant) equal?

Answer 46

K = (1/4)πε_o =8.99 x 10⁹ (Nxm²)/C²

Question 47

Electric field

Answer 47

E=F/q_o = kq/r² f is the force felt by test charge q_o

Question 48

Force generated by electric field

Answer 48

E=E_q1 + E_q2 + E_q3 + ... F=q_oE

Question 49

electric potential energy

Answer 49

U=kqQ/r potential energy between two charges separated by distance r potential energy due to constant electric field U=Vq and U=qED

Question 50

electric potential

Answer 50

V = W/q_o V=kQ/r J/C=NxM/C constant electric field: V=Ed

Question 51

potential difference

Answer 51

Voltage between points a and b = V_b-V_a = W_ab/q_o

Question 52

ε_o

Answer 52

8.85 x 10−12

Question 53

conversion between tesla and gauss and units of tesla

Answer 53

1 Tesla =1 N x s/m x C = 10⁴ gauss gauss is smaller

Question 54

determine total electric current passing through a conductor per unit time

Answer 54

i=Δq/Δt unit is 1 Ampere = 1 C/s

Question 55

magnetic field produced by straight current carrying wire

Answer 55

B=(µ_oi)/2πr

Question 56

magnetic field generated by a circular loop of current carying wire at the center of the loop

Answer 56

B=(µ_oi)/2r

Question 57

Force on a moving charge throguh an external magnetic field

Answer 57

F=qvB sin θ q is charge (including sign) v is the velocity and b is the magnetic field

Question 58

µ_o

Answer 58

permeability of free space = 1.26 x 10^-6 T x m/A

Question 59

force on a current carrying wire in a uniform external magnetic field

Answer 59

F = iLB sin θ i is the current, L is length and b is magnetic field

Question 60

resistance

Answer 60

R=pL/A p is resistivity, L is length and A is cross sectional area

Question 61

ohms law

Answer 61

V = iR

Question 62

actual voltage supplied by a cell to a circuit

Answer 62

V = ε_cell - ir_int r int is the internal resistence = 0 when there is no currentg εcell is voltage supplied

Question 63

Power of a resistor

Answer 63

P=IV = I²R = V²/R

Question 64

total voltage and resistance for resistors in series

Answer 64

Vs=v1 + v2 + v3 + ....+Vn Rs = R 1 + R2 + R3 + ...+ Rn

Question 65

total resistance and voltage when resistors are connected in parallel

Answer 65

Vp=V1 = V2 = V3 =...=Vn 1/Rp=1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Question 66

capacitance

Answer 66

C=Q/V C=ε_o (A/d)

Question 67

Electric field at a point in space between plates of a parallel plate capacitor

Answer 67

E=V/d

Question 68

potential energy stored in a capacitor

Answer 68

U=1/2 CV²

Question 69

increase in capacitance due to a dialectric material

Answer 69

C'=KC

Question 70

voltage and capacitance of capacitors in seris

Answer 70

1/Cs=1/C1 + 1/C2 + 1/C3 + .... Vs=V1 + v2 + v3 + ...

Question 71

voltage and capacitance of Capacitors in parallel

Answer 71

Cp=C1 + C2 + C3 + ... Vp = V1 = V2 = V3 =...

Question 72

rms current

Answer 72

I_rms = I_max/root2

Question 73

rms voltage

Answer 73

Vrms = V_max/root2

Question 74

restoring force of a spring

Answer 74

F=-kx

Question 75

angular frequency of a spring

Answer 75

ω=2πf ω=sqt(k/m)

Question 76

potential energy of a spring

Answer 76

u=1/2kx^2

Question 77

angular frequency of a pendulum

Answer 77

ω=2πf=sqt(g/L)

Question 78

frequency

Answer 78

sqt(1/T) or sqt(ω/2π)

Question 79

spring system kmax occurs at?

Answer 79

x=0

Question 80

pendulum system kmax occurs at?

Answer 80

theta=0 (vertical position)

Question 81

max potential energy of spring system

Answer 81

x=+/- X

Question 82

max potential energy of pendulum

Answer 82

max value of theta

Question 83

max acceleration of spring system

Answer 83

x= +/- X

Question 84

max acceleration of pendulum

Answer 84

max value at theta

Question 85

speed of a wave

Answer 85

v=fλ

Question 86

sound intensity

Answer 86

I = P/A power over area

Question 87

sound level

Answer 87

β=10 log I/I_o

Question 88

calculate new sound level

Answer 88

β_f=β_i + 10 log ( I_f / I_i ) ( If / Ii ) = ratio of final to initial intensity

Question 89

beat frequency

Answer 89

F_beat=|F₁-F₂|

Question 90

doppler effect

Answer 90

f'=[(v±Vd) / (v∓Vs )]

Question 91

wavelength of a standing wave on a string

Answer 91

λ=2L/n

Question 92

frequency of a standing wave on a string

Answer 92

f=nv/2L

Question 93

fundamental frequency or first harmonic

Answer 93

lowest frequency longest wavelength of a standing wave

Question 94

open pipes

Answer 94

act like strings n=number of half waves λ=2L/n f=nv/2L

Question 95

closed pipes

Answer 95

λ=4L/n f=nv/4L

Question 96

speed of light

Answer 96

c=fλ c=3 x 10^8

Question 97

wavelength of red light

Answer 97

760 nm

Question 98

law of reflection

Answer 98

Θ1=Θ2

Question 99

mirror equations

Answer 99

1/o + 1/i=1/f f=(1/2)r

Question 100

magnification

Answer 100

m=-i/o |m| |m|\>1 image is enlarged |m|=1 image is the same size

Question 101

snells law

Answer 101

n1sinΘ=n2sinΘ n=c/v c is the speed of light in a vacuum and v is the speed of light in the medium n for air = 1

Question 102

lens power

Answer 102

P=1/f diopters

Question 103

formula for lenses

Answer 103

1/o+1/i=1/f m=-i/o

Question 104

lensmaker's equation

Answer 104

use for thick lenses 1/f=(n-1)(1/r₁-1/r₂) n is the index of refraction for lens material r1 is the radius of curvature for first and 2nd lens

Question 105

multiple lens systems

Answer 105

for lenses in contact 1/f=1/f1 + 1/f2+1/f3... P= P1 + P2 + P3... for lenses not in contact M=m1 x m2 x m3....

Question 106

peak wavelength at a given temperature

Answer 106

(λ_peak)(T) = 2.9 x 10^-3 peak wavelength means wavelength that radiates greatest energy. not highest wavelength possible (both higher and lower wavelengths will be admitted

Question 107

energy of a photon

Answer 107

E=hf λ=c/f

Question 108

maximum kinetic energy of an electron ejected by an incident photon

Answer 108

Kmax=hf-W

Question 109

energy of an electron with given quantum number in joules

Answer 109

E=-R_H/n^2

Question 110

rydberg constant

Answer 110

2.18 x 10 & -18

Question 111

estimate energy of an electron with given quantum number n in electron volts

Answer 111

E_n=-13.6/n^2

Question 112

change in energy due to absorbtion or emission of a photon

Answer 112

hf=Ef-Ei

Question 113

alpha decay

Answer 113

emission of a helium nuclius

Question 114

beta particle decay

Answer 114

B- decay means nutron becomes a proton 0 B -1

Question 115

positron decay

Answer 115

proton becomes positron and neutron 0 B +1

Question 116

exponential decay

Answer 116

rate = Δn/Δt n=n₀e^-λt λ=ln/half life = 0.693/half life

Question 117

wavelength of violet light

Answer 117

380 nm

Question 118

potential energy of a pendulum

Answer 118

u=mgh

Question 119

doppler effect approximation

Answer 119

Δf/f_s=v/c Δλ/λ_s = v/c