3.6.1 Further mechanics

Question 1

Why is an object moving in a circular path at constant speed accelerating?

Answer 1

It has a constantly changing velocity as it is changing direction, so it must be accelerating

Question 2

What is the force experienced by an object moving in a circle?

Answer 2

The centripetal force

Question 3

Where does the centripetal force act?

Answer 3

Towards the centre of the circle

Question 4

What is angular speed?

Answer 4

The angle an object moves through per unit time

Question 5

What is simple harmonic motion?

Answer 5

When an object’s acceleration is directly proportional to its negative displacement from the equilibrium position, a=-ω²x

Question 6

Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.

Answer 6

Cosine curve

Question 7

Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.

Answer 7

Sine curve

Question 8

Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.

Answer 8

Negative cosine curve

Question 9

Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.

Answer 9

Negative sine curve

Question 10

Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.

Answer 10

Cosine curve

Question 11

Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.

Answer 11

Sine curve

Question 12

Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.

Answer 12

Negative cosine curve

Question 13

Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.

Answer 13

Negative sine curve

Question 14

Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.

Answer 14

Cosine curve

Question 15

What are simple harmonic systems?

Answer 15

Those which oscillate with simple harmonic motion, such as a simple pendulum or a mass-spring system

Question 16

Describe a simple pendulum.

Answer 16

• A small, dense bob hangs from a string attached to a fixed point
• When the bob is displaced by a small angle, and let go, it will oscillate with SHM

Question 17

Why must the angle by which the pendulum is displaced be less than 10°?

Answer 17

The formula is derived using a small angle approximation, so for larger initial angles this approximation is no longer valid, so would not be a good model

Question 18

How many energy transfer cycles are there in an oscillation of a simple harmonic system?

Answer 18

Two

Question 19

Describe the energy transfer of a simple harmonic system.

Answer 19

When the displacement is at a maximum, it has maximum PE and minimum KE, when passing equilibrium it has maximum KE and minimum PE, and at minimum displacement it has maximum PE and minimum KE

Question 20

What does the total energy of a simple pendulum consist of?

Answer 20

Kinetic and gravitational potential energy

Question 21

Describe a mass-spring system.

Answer 21

A mass is attached to the end of a spring, and is pulled down/across a small distance and let go, so it undergoes SHM

Question 22

What is the difference between a vertical and a horizontal mass-spring system?

Answer 22

For a vertical system, kinetic energy is converted to both elastic and gravitational potential energy, whereas for a horizontal system, kinetic energy is converted only to elastic potential energy.

Question 23

What does the total energy of a vertical mass-spring system consist of?

Answer 23

Kinetic energy, and elastic and gravitational potential energy

Question 24

What does the total energy of a horizontal mass-spring system consist of?

Answer 24

Kinetic and elastic potential energy

Question 25

What is damping?

Answer 25

When the energy in an oscillating system is lost to the environment, leading to reduced amplitude of oscillations

Question 26

What are the 3 main types of damping?

Answer 26

Light damping, critical damping and heavy damping

Question 27

What is light/under damping?

Answer 27

Where the amplitude gradually decreases by a small amount each oscillation, and the period is not affected

Question 28

What is critical damping?

Answer 28

Where the amplitude is reduced to zero (returns to equilibrium) in the shortest possible time, without oscillating

Question 29

What is heavy/over damping?

Answer 29

Where the amplitude reduces slower than with critical damping, but also without any additional oscillations

Question 30

How do free vibrations occur?

Answer 30

When no external force is continuously acting on the system, and it oscillates at its natural frequency

Question 31

What is the natural frequency of a system?

Answer 31

The frequency a system oscillates at with free vibrations, where no external force is continuously acting on the system

Question 32

What are forced vibrations?

Answer 32

Where a system experiences an external driving force, causing it to oscillate

Question 33

What is the driving frequency of a system?

Answer 33

The frequency of the external driving force causing a system to oscillate with forced vibrations

Question 34

How does resonance occur?

Answer 34

If the driving frequency is equal to the natural frequency of a system (also known as the resonant frequency)

Question 35

What is resonance?

Answer 35

Where the amplitude of oscillations of a system drastically increase due to gaining an increased amount of energy from the driving force

Question 36

What are examples of applications of resonance?

Answer 36

- Instruments: such as a flute, which has a long tube in which air resonates, causing a stationary sound wave to be formed - Radio: tuned so that their electric circuit resonates at the same frequency as the desired broadcast frequency - Swing: if someone pushes a swing, they provide a driving frequency, which can cause resonance if it’s equal to the resonant frequency and cause the swing to swing higher

Question 37

What is the negative consequence of resonance?

Answer 37

It can cause damage to a structure, such as a bridge when the people crossing it are providing a driving frequency close to the natural frequency, it will begin to oscillate violently witch could be very dangerous and damage the bridge

Question 38

How can the effect of resonance be decreased?

Answer 38

By using damping

Question 39

What is the effect to the resonant frequency of a system as the degree of damping is increased?

Answer 39

- Resonant frequency decreases (shifts left on a graph) - Maximum amplitude decreases - Peak of maximum amplitude becomes wider

Question 40

How is the velocity-time graph related to the displacement-time graph of an object in SHM?

Answer 40

It is the gradient function of the displacement-time graph, as velocity is the derivative of displacement

Question 41

How is the acceleration-time graph related to the velocity-time graph of an object in SHM?

Answer 41

It is the gradient function of the velocity-time graph, as acceleration is the derivative of velocity