A2 - Further Mechanics

Question 1

What type of quantity is momentum?

Answer 1

Vector.

Question 2

What are the units for momentum?

Answer 2

kgms-1 =Ns

Question 3

Define impulse

Answer 3

Change in momentum - F(8)t =m(8)v

f=m(v-u)/t

Question 4

What is the force-time graph for a rocket? What does the area under a F-T graph represent?

Answer 4

Triangular shape.

Area represents impulse - change in momentum.

Question 5

State N3L and explain how this affects a gas molecule on impact with a gas cylinder

Answer 5

When two objects interact, they exert equal and opposite forces on each other.

Gas molecule exerts the same force on cylinder on impact as cylinder exerts on it, there is just more of a visible effect because the gas molecule is accelerated more due to its lower mass.

Question 6

Define an inelastic collision.

Answer 6

Momentum is conserved, kinetic energy is not

Question 7

Define an elastic collision

Answer 7

Momentum and kinetic energy is conserved

Question 8

Give 2 examples of inelastic collisions

Answer 8

Explosion, coalescence

Question 9

Give an example of an elastic collision

Answer 9

Hard material rebounding

Question 10

What is the rule for conservation of momentum?

Answer 10

It is always conserved unless external forces act on the object.

Question 11

Is an explosion elastic or inelastic?

Answer 11

Inelastic.

Question 12

What is the kinetic energy just after an explosion of two trolleys

Answer 12

It is equal to the kinetic energy stored in the springs = 0.5kl^2

Question 13

What are the units for angular displacement?

Answer 13

radians

Question 14

What are the units for angular velocity? Which greek letter is used to represent it?

Answer 14

rads-1

omega

Question 15

In which direction does the force need to act for an object in circular motion?

Answer 15

Towards the centre

Question 16

When an object is in vertical circular motion, when is the force towards the centre maximum?

Answer 16

When the object is at the bottom of the circle, as it does not have mg working in the same direction and has to overcome this to give a constant centripetal acceleration.

Question 17

How do you find angular velocity?

Answer 17

angular displacement/time (rads^-1)

Question 18

What is frequency?

Answer 18

Number of oscillations/revolutions per second

Question 19

What is period?

Answer 19

The time taken for one oscillation/revolution

Question 20

At which point is the string of a vertically rotating object most likely to break and why?

Answer 20

The bottom, as the tension causing the centripetal acceleration must counter the weight of the object, so this is where the maximum force is.

Question 21

What is damping?

Answer 21

Application of friction to an oscillating system that causes the amplitude to decrease over multiple periods.

Question 22

What is heavy damping?

Answer 22

A large frictional force is applied that causes the amplitude to decrease quickly

Question 23

What is light damping?

Answer 23

A small frictional force is applied such that the amplitude decreases slowly.

Question 24

What is critical damping?

Answer 24

Where the frictional force is such that the oscillation is reduced to zero as quickly as possible.

Question 25

What is free oscillation?

Answer 25

Where the oscillator is released and allowed to oscillate at its natural frequency.

Question 26

In a physical system, why does the amplitude not constantly increase?

Answer 26

Damping limits the effects of the increasing amplitude.

Question 27

What happens when an oscillator is damped?

Answer 27

The period is not affected, the amplitude decreases. It is an exponential decay, so the follows a constant ratio.

Question 28

For a simple pendulum system, where does the resultant force act?

Answer 28

Towards the equilibrium position.

Question 29

Which two things change the frequency of a mass-spring system?

Answer 29

extra mass

Weaker springs

Question 30

What are forced oscillations?

Answer 30

An oscillating system will respond to forced oscillations depending on the frequency of the driving oscillation.

Question 31

What is resonance?

Answer 31

when the driving (applied) frequency equals the natural frequency, the oscillator is (pi)/2 radians out of phase with the driver

Question 32

What is the phase difference between the driver and oscillator under resonant frequency?

Answer 32

pi/2

Question 33

What is the phase difference between driver and oscillator when not under natural frequency?

Answer 33

increases from pi/2 to pi as driving frequency increases.

Question 34

In barton’s pendulums, what does the amplitude of each pendulum depend on, including the one of the same length as the driver?

Answer 34

Driver responds in resonance because the natural frequency of both match, the others oscillate depending on proximity to the driver

Question 35

What is the shape of kinetic energy vs displacement for a pendulum?>

Answer 35

Inverted parabola

Question 36

If two spheres both have their radii doubled, what happens to the force?

Answer 36

Each mass increases by 8x, so the force increase due to the mass is 64x

This is divided by an increase in radius of 2x, so r^2=0.25, hence 64/0.25= 16x increase

Question 37

When an object is in SHM on a spring, what is the overall direction of the force at the top and bottom of the stroke?

Answer 37

top - downwards due to gravity

Bottom - upwards due to force in spring (proportional to extension)

Question 38

What are the principles of conservation of energy and momentum and how do they apply to a probe exhausting a capsule to increase velocity?

Answer 38

Energy is always conserved, but in an explosion, is converted into other forms, such as heat. Momentum is always conserved unless an external force acts.

In an explosion of this kind, since momentum is a vector, and there is no vertical momentum, the capsule is exhausted directly backwards.

Question 39

What happens when the driving frequency increases above resonant frequency?

Answer 39

Phase difference increases from pi/2 to pi rad out of phase