Physics 151 – Exam Equation Sheet

Exam 1 Equations

Unit Conversions 1 m = 1.094 yd = 3.281 ft = 39.4 in 1 mile = 1609 m 1 in = 2.54 cm Constants g = 9.81 m/s2 = 32.0 ft/s2

c = 2.99 x 108 m/s Geometric Formulae Circle

2

2C r

A r

Rectangle

2P l w

A l w

Cube

2

3

6A l

V l

Sphere 2

3

4

4

3

A r

V r

Cylinder 2

2

2 2A r rl

V r l

Triangle Trigonometry

sin

cos

opp

hyp

adj

hyp

opptan

adj

1-D Kinematics

distanceaverage speed

elapsed time

displacementaverage velocity

elapsed time

If a = 0 then x vt If a ≠ 0

then

0

0

20

2 20

1

21

2

2

v v at

x v v t

x v t at

v v ax

Horizontal Range

20 sin 2

vR

g

Exam 2 Equations Friction Static Friction

Kinetic Friction

Springs Hook’s Law

Centripetal Acceleration Newton’s 2nd Law

Torque

Torque Equilibrium

k kf N

s sf N

xF kx

2

c

va

r

F ma

sinrF

0

Exam 3 Equations Work

Work-Energy Theorem

Energy

Kinetic Energy 21

2KE mv

Gravitational Potential Energy PE mgh

Elastic Potential Energy 21

2PE kx

Conservation of Energy

i i f fKE PE KE PE

Work Done by NonConservative Forces

NCW KE PE

Momentum p mv

Impulse

aveI F t p

cosW Fd

2 21 1

2 2total f iW KE mv mv

Exam 4 Equations Simple Harmonic Motion Position vs. Time

2cos

1

x A tT

fT

Mass on a Spring

21

2

2

Elastic

F kx

PE kx

mT

k

Pendulum 2L

Tg

Waves v f Waves on a String

Tv

where μ is the linear density

(mass/length) Wave Formula

2 2, cosy x t A x t

T

Sound vSound = 343 m/s (at room temperature)

24

P PI

A r

100

22 1 10

1

10 log

10log

I

I

I

I

where I0 = 10-12 W/m2

Standing Waves String

1, 2,3...2 2n

v n Tf n n

L L

Open-Closed Pipe

1,3,5...4n

vf n n

L

Open-Open Pipe 1,2,3...2n

vf n n

L

Fluids Density M

V

Pressure F

PA

Pa = 1.01 x 105 Pa Pressure at Depth aP P gh

Pascal’s Principle – An external pressure applied to an enclosed fluid is transmitted unchanged to every point within the fluid

1 2

1 2

1 2

P P

F F

A A

Archimedes’ Principle – An object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of fluid displaced by the object.

B fl flF V g

Equation of Continuity

1 1 2 2v A A v

Bernoulli’s Equation

2 21 1 1 2 2 2

1 1

2 2P v gy P v gy

Exam 5 Equations Temperature Scales

932

5273.2

F C

K C

T T

T T

Thermal Expansion

0

0

L L T

V BV T

For many substances β=3α Substance Coefficient of

Linear Expansion, α (Cº-1) Lead 29 x 10-6 Aluminum 24 x 10-6 Brass 19 x 10-6 Copper 17 x 10-6 Steel 12.2 x 10-6 Concrete 12 x 10-6 Thermal Conductivity Q A T A

t L L

Substance Thermal Conductivity

κ (W/(m·Cº) Silver 417 Copper 395 Gold 291 Aluminum 217 Steel 66.9 Lead 34.3 Ice 1.6 Concrete 1.3 Glass 0.84 Wood 0.10 Air 0.0234 Calorimetry

Q mc T Substance Specific Heat c

(J/(kg·Cº) Water 4186 Ice 2090 Steam 2010 Air 1004 Aluminum 900 Glass 837 Steel 448 Copper 387 Silver 234 Gold 129 Lead 128 One can convert c values to cal/g-Cº by dividing by 4186 Latent Heats

f

v

Q mL

Q mL

For water these values are: Lf = 33.5 x 104 J/kg = 79.7 cal/g Lv = 32.6 x 105 J/kg = 540 cal/g One can convert L values to cal/g by dividing by 4186 Ideal Gas Law PV = nRT, PV = NkT where n = amount of substance and N the number of particles, R=8.314 J/mol·K NA=6.02 1023 particles k =1.38 10-23 J/K n = N / NA and n = m/M where m is the total mass and M the molar mass

Young’s Modulus

0

0

F LStress Strain

A L

FLStressY

Strain A L

Thermal Stress

0

0

FL LY T

A L L

FY T

A

Substance Young’s Modulus Y

(N/m2) Tungsten 36 x 1010 Steel 20.1 x 1010 Copper 11 x 1010 Brass 9.0 x 1010 Aluminum 6.9 x 1010 Pyrex 6.2x 1010 Lead 1.6 x 1010 Substance Molar mass (g/mol)

H2 2.016 O2 32

CO2 44.01 N2 28.01

Methane, CH4

16.04

CO 28.01 Air 28.966

Water vapor

18.02

Exam 6 Equations

Photons

h = 6.626 10-34 J·s c=2.99 108 m/s Doppler Shift

Reflection

Spherical Mirrors

Refraction

Thin Lenses

Electric Charge Coulomb’s Law

1 22

q qF k

R

where k = 8.99 109 N·m2 /C2 Fundamental charge e = 1.602 x 10-19 C Electric Circuits

22

V IR

VP IV I R

R

Resistivity

LR

A

Resistors Series 1 2 ...effR R R

Parallel 1 2

1 1 1...

effR R R

c f

hcE hf

' 1u

f fc

i r

1

21

21 1 1

convex

concave

o i

i i

o o

f R

f R

d d f

h dm

h d

1 1 2 2

2

1

sin sin

sin c

n n

n

n

1 1 1

o i

i i

o o

d d f

h dm

h d