Mechanics and Special Relativity

Question 1

What is A•B physically?

Answer 1

The magnitude of A multiplied by the component of B in the direction of A.

Question 2

What A•B mathematically?

Answer 2

|A||B|cosx

Question 3

Is A•B = B•A?

Answer 3

Yes

Question 4

A•B in terms of components?

Answer 4

AxBx + AyBy + AzBz

Question 5

A•A=?

Answer 5

(|a|)^2

Question 6

What is Einstein’s first postulate?

Answer 6

The laws of physics are the same in every inertial frame of reference.

Question 7

What is Einsteins second postulate?

Answer 7

The speed of light in vacuum is the same in all inertial frames of reference and is independent of the source.

Question 8

What is the speed of light?

Answer 8

2.998x10^8

Question 9

What 3 conclusions are drawn from Einsteins postulates?

Answer 9

• No absolute ruler length
• No absolute clock
• Simultaneity depends on the observers.

Question 10

What is the Lorentz factor (equation)?

Answer 10

Y=(1-(u/c)^2)^-1/2

Question 11

Do moving clocks tick fast or slow?

Answer 11

Slow

Question 12

Time dilation equation

Answer 12

t=y•t0

Question 13

Why can massive objects not move at the speed of light?

Answer 13

Because it would require infinite energy.

Question 14

What is proper time?

Answer 14

Time as measured by an observer with a stationary clock (at the same location as the observer).

Question 15

What is proper length?

Answer 15

The length of a body in a reference frame at which the body is at rest.

Question 16

Do moving bodies contract or lengthen according to a stationary observer?

Answer 16

Contracts

Question 17

Equation of length contraction?

Answer 17

L = L0/Y

Question 18

How are lengths parallel and perpendicular to the direction of motion affected?

Answer 18

Parallel - contracted by factor of 1/y

Perpendicular - unaffected

Question 19

What is a unit vector?

Answer 19

A vector that has magnitude 1

Question 20

What’s Newton’s first law?

Answer 20

In the absence of a net force a body at rest will remain at rest, bodies in uniform motion will remain in uniform motion at constant velocity.

Question 21

What’s Newton’s second law?

Answer 21

F=ma

Question 22

What’s Newton’s third law?

Answer 22

For every action, there is an equal and opposite reaction.

Question 23

Evaluate the frictional force on a body.

Answer 23

F = uN in opposite direction to direction of motion.

Question 24

Which is bigger? Coefficient of friction when static or in motion?

Answer 24

Static

Question 25

Fluid resistance at low velocity?

Answer 25

F = kV where k is viscosity

Question 26

Fluid resistance at high velocity?

Answer 26

F = DV^2 where D is drag.

Question 27

Work done =?

Answer 27

Wd = S F•ds | Path

Question 28

How is the work done on an object and its kinetic energy related.

Answer 28

Wd = 🔼KE

Question 29

What's Hooke's law?

Answer 29

Force on a mass due to a spring = -kx

Question 30

What is the potential energy of a spring compressed or stretched by x from equilibrium?

Answer 30

U = (kx^2)/2

Question 31

What is the speed of a mass compressed or stretched by X from equilibrium when it passes through equilibrium after release?

Answer 31

V=X•sqrt(k/m)

Question 32

Equation of momentum?

Answer 32

P=mv

Question 33

How does force affect momentum?

Answer 33

F = dP/dt

Question 34

What is impulse?

Answer 34

🔼P = F x 🔼t for small 🔼t

Question 35

What is a perfectly elastic collision?

Answer 35

Bounce off, KE is conserved

Question 36

What is a perfectly inelastic collision?

Answer 36

Stick together, energy dissipated into deformation.

Question 37

Velocity of the centre of mass =?

Answer 37

V = Ptotal/M

Question 38

What is the change in velocity of rocket of mass M ejecting gas of mass m at speed v?

Answer 38

🔼V = mv/M-m

Question 39

What is the acceleration of a rocket that is constantly ejecting gas at rate of dM/dt = c?

Answer 39

a= - vgas/M * c

Question 40

Calculate angular frequency from linear speed and radius

Answer 40

w = V/r

Question 41

Calculate the frequency of rotation from the angular frequency.

Answer 41

f=w/2pi

Question 42

What is the centripetal acceleration of an object (equation)?

Answer 42

a = w^2*r towards centre of circle

Question 43

What is the acceleration of a mass oscillating on a spring?

Answer 43

a = -kx/m

Question 44

For a small x what's the approximation for cosx?

Answer 44

1 - x^2/2

Question 45

For small X what's the approximation of sinx?

Answer 45

X

Question 46

What's the angular frequency of a pendulum of length L?

Answer 46

w = sqrt(g/L)

Question 47

What's the frequency of a pendulum of length L?

Answer 47

T = 2pi*sqrt(L/g)

Question 48

What is a physical pendulum?

Answer 48

Any real pendulum that uses an extended body.

Question 49

What is the angular frequency of a physical pendulum?

Answer 49

w = sqrt(I/mgd) where I is moment of inertia and d is distance from rotational axis to centre of gravity.

Question 50

What is the force on a mass undergoing damped SHM?

Answer 50

F = -kx -bV

Question 51

What is the decay timescale in damped SHM?

Answer 51

The time for the amplitude to be reduced by a factor of e.

Question 52

What is the angular frequency of a slightly damped oscillator?

Answer 52

w' = sqrt(k/m - b^2/4m^2)

Question 53

What is the amplitude of a forced oscillator?

Answer 53

A = ______F_max_______________ Sqrt((k-mw^2)^2 + (bw)^2 Where w is driving angular frequency and b is the damping constant.

Question 54

What is the classical mechanics limit?

Answer 54

V