Further Mechanics

Question 1

Define centripetal acceleration.

Answer 1

the acceleration of an object moving in circular motion. Any object in circular motion must have an acceleration since the direction of the object, therefore the velocity of the object, is constantly changing.

Question 2

Denise centripetal force.

Answer 2

The resultant force responsible for an object moving in circular motion. Centripetal forces always act towards the centre of the objects rotation.

Question 3

Define angular speed

Answer 3

A measure of the speed of the objects angular rotation. It is equal to the frequency of rotation multiplied by 2π.
The angle an object moves through per unit of time.

Question 4

When does an object experience simple harmonic motion?

Answer 4

when acceleration is directly proportional to displacement and is in the opposite direction. These conditions can be shown through the relationship:

a is directly proportional to the negative displacement.
a = -ω^2x

Question 5

How is the v - t graph derived from the x - t graph? How is the a - t graph derived from the x - t graph?

Answer 5

The gradient

Question 6

How can s - t v - t and a - t graphs be produced?

Answer 6

Data loggers.

Question 7

Sketch a x - t graph

Answer 7

Cosine graph with A being max value and -A being minimum value.

Question 8

Sketch a v -t graph

Answer 8

A sine graph which starts from the negative

maximum value is ωA
Minimum value is -ωΑ

Question 9

Sketch a graph of the a - t.

Answer 9

Cosine graph which starts do=eom negative.

Max value of ω^2Α
Min value of ω^2Α

Antiphase with displacement

Question 10

What are simple harmonic systems?

Answer 10

Those which oscillate with simple harmonic motion.

Simple pendulum
Mass-spring system

Question 11

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

Answer 11

Because during the derivation of the Time period formula for a simple pendulum a small angular approximation is used and so for larger initial angles this approximation is no longer valid, and would not be a good model.

Question 12

What energies are present in the oscillations of a simple pendulum?

Answer 12

Its gravitational potential energy is transferred to kinetic energy and then back to gravitational potential energy and so on.

Question 13

For a vertical mass spring system what is the kinetic energy converted into?

Answer 13

Both elastic potential energy and gravitational potential energy.

Question 14

What is kinetic energy converted into for a horizontal mass-sporting system?

Answer 14

Only elastic potential energy.

Question 15

Where in its cycle will a system have its maximum amount of potential energy?

Answer 15

At the amplitude of its oscillations.

Question 16

when is the potential energy converted to kinetic energy?

Answer 16

As it moves towards the equilibrium position.

Question 17

Where is kinetic energy at its maximum?

Answer 17

At the equilibrium position.

Question 18

How does the total energy of the system remain constant?

Answer 18

Because air resistance is negligible. Other wise it is lost as heat.

Question 19

What is damping?

Answer 19

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

Question 20

What are the three main types of damping?

Answer 20

Light damping
Critical damping
Heavy damping

Question 21

What is light damping?

Answer 21

Also known as under-damping and this is where the amplitude gradually decreases by a small amount each oscillation

Question 22

What is critical damping?

Answer 22

This reduces the amplitude to zero in the shortest possible time (without oscillating).

Question 23

What is heavy damping?

Answer 23

Over-damping, and this is where the amplitude reduces slower than with critical damping, but also without any additional oscillations.

Question 24

What are free vibrations?

Answer 24

Oscillations that are not caused by a driver. An object will naturally oscillate at its natural frequency

Question 25

What are forced vibrations?

Answer 25

Where a system experiences an external driving force which causes it to oscillate. Occur when no external force is continuously acting on the system, therefore the system will oscillate at its natural frequency.

Question 26

What is resonance?

Answer 26

Resonance occurs when the frequency of oscillations is equal to the natural frequency of the oscillating system. The rate of energy transfer is at a maximum during resonance.

Question 27

What are some applications that uses resonance?

Answer 27

Flute - long tube in which air resonates, causing a stationary sound wave to be formed. Radio - tuned so that an electric circuit resonates at the same frequency as the desired broadcast frequency. Swing - if someone pushes you on a swing they are providing a driving frequency, which can cause resonance if it’s equal to the resonant frequency and cause you to swing higher.

Question 28

What are free vibrations?

Answer 28

Repeated up and down oscillations, at the frequency of a driver. The amplitude of oscillation is small at high frequencies and large at low frequencies.

Question 29

How can damping be used to decrease the effect of resonance?

Answer 29

As the degree of damping increases, the resonant frequency decreases and the maximum amplitude decreases and the peak of maximum amplitude becomes wider. Shown in the graph of amplitude against resonant frequency.