Equations

Question 1

Displacement (not given velocity)

Answer 1

dx = Vox*dt + (1/2)at²

Question 2

Velocity (not given displacement)

Answer 2

Vx = Vox +ax*dt

Question 3

Displacement (not given acceleration)

Answer 3

dx = 1/2(Vox + Vtx)*dt

Question 4

Velocity (not given time)

Answer 4

Vx²=Vo² + 2a*dx

Question 5

Short cut for how far an object will fall in a given time

Answer 5

dy = 5t² meters

So in 1 second, an object will fall about 5 meters

Question 6

What is the time it takes for a projectile to reach its apex?

Answer 6

t = Voy/g

Question 7

What is the range of a projectile?

Answer 7

R = 2Vox*Voy/g

= 2Vo²sin(2Ø)/g

**This is only true when initial and final height are the same

Question 8

Newton’s second law

Answer 8

F=ma

Question 9

Weight

Answer 9

W = m*g

Question 10

Newton’s third law

Answer 10

ΣF = 0

Every action has an equal and opposite reaction

Useful for pulley problems, collisions … etc.

Question 11

Force of gravity

Answer 11

F = GM₁M₂/r²

Question 12

Apparent weight read by a scale in an elevator

Answer 12

S = W + ma = W(1 + a/g)

S is apparent weight read by scale, W is actual weight

Question 13

Arc length

Answer 13

S = Ø*r

Question 14

Angular velocity

Answer 14

omega = dØ/dt = V/r

Question 15

Centripetal acceleration

Answer 15

a = v²/r = w²r

w=angular velocity

Question 16

angular velocity in uniform circular motion

Answer 16

w = 2pi/T

T is period, time to complete one revolution

Question 17

Centripetal force

Answer 17

Fcent = mv²/r

Question 18

Kepler’s law of orbital motion

Answer 18

T² = (4pi²/GM)R³

Objects move faster and experience greater force when they are closer to the object which it is orbiting

Question 19

Static friction

Answer 19

fs = Mu_s*N

Mu_s= coefficient of static friction

N = normal force = m*g

Question 20

Work due to displacement of an object

Answer 20

W = F*cos(Ø)*dx

Negative work signifies an object losing energy to its surroundings, ex: friction

Question 21

Work-Energy relationship

Answer 21

W_total = KE_final - KE_initial

Question 22

Object starting at rest, sliding down an inclined plane

Answer 22

vf² = 2gh

** angle of incline does not affect the final speed

Question 23

Gravitational potential energy

Answer 23

dPE = mg(dh)

dPE = change in potential energy

dh = change in heigh

Question 24

Power

Answer 24

P = dW/dt

Power is the rate of transferring energy, the rate of doing work

Question 25

Momentum

Answer 25

p = mv

Question 26

collisions

Answer 26

m₁v_1i +m₂v_2i = m₁v_1f +m2v_2f

Question 27

Impulse

Answer 27

J =F*dt = mv_f - mv_i

impulse is the change in momentum

Question 28

inelastic collision

Answer 28

m1v1i = (m1 + m2)vf

Question 29

elastic collision

Answer 29

m₁v₁=m₂V_2f

Question 30

Torque

Answer 30

Tau = rFsin(Ø)

Question 31

Mechanical Advantage

Answer 31

Weight of object / Applied Force needed

Question 32

Hooke’s Law

Answer 32

F = -kx

springs

Question 33

Spring potential energy

Answer 33

U = 1/2 kx²

Question 34

Period of spring

Answer 34

T = 2pi *sqrt(m/k)

Question 35

Potential energy of a pendulum

Answer 35

U = mgL*(1-cosØ)

Question 36

Period of a pendulum

Answer 36

T = 2pi*sqrt(L/g)

Question 37

Velocity of a wave

Answer 37

v = wavelength*frequency

Question 38

velocity of a transverse wave in terms of tension

Answer 38

v = sqrt(T/mu)

T is tension, mu is mass per unit length

Question 39

frequency of beats

Answer 39

fbeat = abs(f2-f1)

Question 40

Intensity of sound

Answer 40

I = Power/Area

Question 41

Intensity level

Answer 41

B = 10*log(I/Io)

Question 42

Relationship between distance from source and sound intensity level

Answer 42

Every time distance increases by a factor of 3.2, the intensity drops by a factor of 10, thus lowers by 10 dB

Question 43

Doppler effect

Answer 43

f_L = ((v+-v_L)/(v+-v_S))*f_s

Question 44

Pascal’s Principle

Answer 44

P1-P2 = pg*dh

p = fluid density

dh = difference in depth between P1 and P2

Question 45

Buoyancy force

Answer 45

Fb = p_fluid*V_{fluiddisplaced}*g

p_fluid is fluid density

Question 46

Specific Gravity

Answer 46

SG = W_app/W_inH2O = p_obj/ p_H2O

Question 47

Poiseuilles Principle

Answer 47

P1-P2 = (4nL/r²)v

n = coefficient of viscosity

v is highest in center of pipe and close to zero at the sides

Question 48

Flow rate in a pipe

Answer 48

Q = (pi*r⁴/8nL)*(P1-P2)

if r is doubled, Q will increase by factor of 16

Question 49

Continuity equation for pipe with changing diameter

Answer 49

Q = A1v1 = A2v2

smaller area, faster speed

Question 50

Bernoulli’s Equation

Answer 50

P₁ + 1/2pv₁² + pgh₁ = P₂ +1/2pv₂² + pgh₂

In otherwords:

Constant = P_{against inner walls} + 1/2pv² +pgh

Question 51

Turbulence

Answer 51

Nr = 2pvR/n

Nr = Reynolds number

Nr<2000 is laminar flow

Nr>3000 is turbulent flow

Question 52

Stress

Answer 52

Stress = F/A

ex: tension, compression

Question 53

Strain

Answer 53

Strain = dL/L

measure of deformation of material

Question 54

Young’s modulus

Answer 54

Y = stress/strain = (F/A)/(dL/L)

Question 55

Coulomb’s Law

Answer 55

F = k(q₁*q₂)/r²

Question 56

Electric Field

Answer 56

E = F/q

Question 57

Electrical potential energy in terms of changing separation between charges

Answer 57

EPE = kq1q2(1/rf - 1/ri)

Question 58

Electrical potential energy in terms of moving particle through voltage difference

Answer 58

EPE = qV

Question 59

Effect of dielectric on electrical force

Answer 59

Fmedium =1/K*(kq1q2/r²)

K = dielectric constant

Question 60

Dipole moment

Answer 60

P = qL

q= product of charge

L = distance between charges

Question 61

Magnetic force

Answer 61

F = gvBsin(Ø)

Question 62

Faraday’s Law

Answer 62

emf = -dI_B/dt

dI_B = flux