Mechanics

Question 1

Define impulse

Answer 1

F x t

Question 2

Derive the impulse-momentum principle

Answer 2

F = ma
a = (v - u)/t
F = m(v - u)/t
Ft = mv - mu

Question 3

What is the equation for momentum conservation for two particles colliding?

Answer 3

m1u1 + m2u2 = m1v1 + m2v2

Question 4

Equation for work done

Answer 4

W = Fs

Question 5

Equation for potential energy

Answer 5

W = mgh

Question 6

Equation for friction

Answer 6

Fr = μR

Question 7

Equation for kinetic energy

Answer 7

Ek = 1/2 mv^2

Question 8

Define principle of conservation of mechanical energy

Answer 8

When no external forces (other than gravity) do work on a particle during its motion, the sum of the particle’s kinetic and potential energy remains constant

Question 9

Define work-energy principle

Answer 9

The change in the total energy of a particle is equal to the work done on the particle

Question 10

How do you work out a particle’s weight components on a slope of angle θ?

Answer 10

Component down slope is mgsin(θ)

Component perpendicular to slope is mgcos(θ)

Question 11

What is power?

Answer 11

Rate of doing work

Question 12

Power equation for work

Answer 12

P=E/t

Question 13

Power equation for moving particle

Answer 13

P=Fv

Question 14

Tension equation for stretched spring

Answer 14

T = kx

Question 15

Hooke’s law equation

Answer 15

T = λx/l

Question 16

Work done stretching a spring equation

Answer 16

W = 1/2 λx^2/l

Question 17

What is elastic potential energy?

Answer 17

Equal to the work done to stretch the spring

Question 18

What is Newton’s law of restitution for two particles colliding?

Answer 18

e = speed of separation/speed of approach
e = (v2 - v1)/(u1 - u2)

Question 19

What is Newton’s law of restitution for a particle colliding with a smooth plane?

Answer 19

e = speed of rebound/speed of approach

Question 20

What is the range of values for coefficient of restitution?

Answer 20

0 =< e =< 1

Question 21

What does elastic collision mean?

Answer 21

Total kinetic energy is constant

Question 22

If a collision is inelastic, what is the equation for loss of kinetic energy?

Answer 22

(1/2 m1u1^2 + 1/2m2u2^2) - (1/2 m1v1^2 + 1/2m2v2^2)

Question 23

When a particle collides obliquely with a surface, in which direction does the impulse act?

Answer 23

Perpendicular to the surface

Question 24

A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the equation for the component of velocity parallel to the surface?

Answer 24

v cos(β) = u cos(α)

Question 25

A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the equation for the component of velocity perpendicular to the surface?

Answer 25

v sin(β) = eu sin(α)

Question 26

A particle hits a surface making angle α at speed u, and rebounds at speed v making angle β. What is the angle of deflection?

Answer 26

α + β

Question 27

When a particle collides obliquely with a surface, and the speed before and after are given as vectors, how can you find the angle of deflection?

Answer 27

cos(θ) = (u.v)/(|u| x |v|)

Question 28

When two particles collide obliquely, and one is originally stationary, what can be said about the stationary particle afterwards?

Answer 28

It will move parallel to the line of centres

No component of speed perpendicular to the line of centres