Module 1: Mathematics & Mechanics

Question 1

If x = a^y , y= ?

Answer 1

y = log(subscript a)x

Question 2

What does the area under a graph represent?

Answer 2

The axes multiplied together

E.g. velocity time graph
Area underneath= displacement

Question 3

What does sin θ ≈ ?

Answer 3

θ

Question 4

What does cos θ ≈ ?

Answer 4

1

Question 5

What does tan θ ≈ ?

Answer 5

θ

Question 6

Scalar quantities

Answer 6

Quantities which are described only by magnitude

Question 7

Vector quantities

Answer 7

Quantities which are described by magnitude and direction

Question 8

How to solve vector subtraction problem

Answer 8

Add vectors head to tail, but flip subtracted vector.

Find resultant vector using trigonometry.

Question 9

SI unit for temperature

Answer 9

Kelvin K

Question 10

How are v, d and t related?

Answer 10

d (or x) = vt

Question 11

Acceleration due to gravity =

Answer 11

10 ms^-2

Unless specified otherwise

Question 12

Relative velocity

Answer 12

How fast the distance between two objects changes

Question 13

Newton’s first law

Answer 13

Objects continue at rest- or constant velocity- unless an external force acts upon them.

Question 14

Newton’s second law

Answer 14

An external force gives the object an acceleration proportional to the force

F = ma

Question 15

Newton’s third law

Answer 15

Forces come in equal and opposite pairs

Question 16

Units of force

Answer 16

Newtons N

Question 17

In Newton’s third law, when do the equal and opposite forces act?

Answer 17

At the same time

Question 18

T (kinematics)

Answer 18

Period: time taken to travel around a circle

Question 19

Circumference equation

Answer 19

2πr

Question 20

Area of circle

Answer 20

πr^2

Question 21

Centripetal force

Answer 21

F = mv^2/r

Question 22

What conditions does the centre of mass fulfil? (3)

Answer 22

Mass one one side balances mass on the other

Forces equal due to symmetry

The object can balance on the point

Question 23

Centre of gravity

Answer 23

Point through which an objects entire weight appears to act

Question 24

Friction

Answer 24

Force between two surfaces. Acts parallel to them

Question 25

Do surfaces applying friction forces to each other touch?

Answer 25

No- due to electrostatic forces

Question 26

In which direction does friction act?

Answer 26

Opposite to the objects relative motion. Parallel to surface

Question 27

f(subscript max) = ?

Answer 27

μN Where μ = coefficient of friction And N = normal force (e.g. mg)

Question 28

Does friction depend on area?

Answer 28

No

Question 29

Air resistance

Answer 29

Atmospheric friction/ drag due to pushing air away

Question 30

As velocity increases, what happens to air resistance?

Answer 30

Increase

Question 31

Equation relating CW and CCW torques

Answer 31

Fd = Fd

Question 32

Class one lever

Answer 32

Load fulcrum effort

Question 33

Class two lever

Answer 33

Effort load fulcrum

Question 34

Class three lever

Answer 34

Load effort fulcrum

Question 35

Describe kinetic energy

Answer 35

The measure of an objects capability to do work because of its motion

Question 36

Units of energy

Answer 36

Joules J

Question 37

Units of work

Answer 37

Joules J

Question 38

Describe potential energy

Answer 38

A measure of an objects potential capability to do work because of its position

Question 39

Two types of microscopic potential energy

Answer 39

Chemical potential energy | Nuclear potential energy

Question 40

Mechanical energy

Answer 40

Total energy inside a system

Question 41

Dissipating forces

Answer 41

Energy from the system which is lost to the surroundings

Question 42

Is mechanical energy conserved?

Answer 42

No, but total energy is. (Just not of the system itself)

Question 43

Units of power

Answer 43

Watts W

Question 44

Efficiency equation

Answer 44

η = W out / E used

Question 45

How do machines increase entropy of the universe?

Answer 45

Energy dissipates

Question 46

Δp

Answer 46

Impulse/ change in momentum

Question 47

Units of momentum

Answer 47

kg ms^-1

Question 48

Force is the transfer of ___?

Answer 48

Momentum

Question 49

Inelastic collision

Answer 49

Momentum is conserved, kinetic energy is not

Question 50

Elastic collisions

Answer 50

Both momentum and kinetic energy are conserved

Question 51

Four steps to solving a collision problem

Answer 51

# Define a system of interest Draw the system before and after Decide which direction is positive/ break into components Determine if collision is elastic or inelastic

Question 52

Sticky inelastic collision

Answer 52

Objects stick together after they have collided

Question 53

If kinetic energy is conserved during a collision, what can we infer about the relative speeds of the objects?

Answer 53

The relative speed of the objects before the collision = relative speed of the objects after v1i - v2i = - (v1f - v2f)

Question 54

Approach velocity

Answer 54

Velocity of one object as seen by the other before a collision

Question 55

Recoil velocity

Answer 55

Velocity of one object as seen by the other after a collision

Question 56

When spring is stretched/ compressed to the max, what’s going on energy wise?

Answer 56

At maximum potential energy Kinetic energy = 0

Question 57

At equilibrium position, how much potential energy does a spring have?

Answer 57

0 KE= TE

Question 58

Transverse wave

Answer 58

Oscillation is perpendicular to propagation

Question 59

Longitudinal waves

Answer 59

Oscillation is in direction of propagation