Further Mechanics

Question 1

What is the centripetal force

Answer 1

The resultant force that causes acceleration

Question 2

What direction does the centripetal force act

Answer 2

Towards the centre of the circle

Question 3

Define angular speed

Answer 3

The angle turned per unit time

Question 4

When is an object experiences simple harmonic motion

Answer 4

When its acceleration is directly proportional to its displacement and is in the opposite direction

Question 5

Give the equation for acceleration

Answer 5

A = - w^2 x

Question 6

For a simple pendulum what is the formula for displacement

Answer 6

X = A cos (wt)

Question 7

For a simple pendulum what is the formula for velocity

Answer 7

V = +/- w (A^2 - x^2)^1/2

Question 8

What graph does displacement have

Answer 8

Sin graph

Question 9

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

Answer 9

The derivation of the formula uses small angle approximations, so for larger angles the approximation isn’t valid

Question 10

Describe the energy transfers for a vertical spring system

Answer 10

Kinetic is converted to elastic potential and gravitational potential energy

Question 11

Describe the energy transfers in a horizontal spring system

Answer 11

Kinetic is converted to elastic potential energy

Question 12

For a simple harmonic motion system when is velocity greatest

Answer 12

At the centre of oscillations

Question 13

Why are the 3 types of damping

Answer 13

• light damping
• heavy damping
• critical damping

Question 14

Describe light damping / under damping

Answer 14

Amplitude is gradually decreased by a small amount each oscillation

Question 15

Describe critical damping

Answer 15

This reduces the amplitude to 0 in the quickest time possible without oscillating

Question 16

Describe heavy damping / over damping

Answer 16

Amplitude reduces slower than critical damping, but without any additional oscillations

Question 17

When do free vibrations occur

Answer 17

When no external force acts continuously on a system, so is oscillated with its natural frequency

Question 18

When does resonance occur

Answer 18

When the driving frequency = the natural frequency of the system

Question 19

What is resonance

Answer 19

When the amplitude of oscillations of a system drastically increases as it gains more energy from the driving force

Question 20

Give 3 applications of resonance

Answer 20

• instruments
• radio

Swing

Question 21

Describe how resonance can be used for instruments

Answer 21

The air in woodwind instruments resonates, so a stationary wave is formed

Question 22

Describe how resonance works in a radio

Answer 22

They’re tuned so the electrical circuit vibrates at the same frequency as the broadcasting frequency

Question 23

Describe how resonance works for a swing

Answer 23

If the person pushing ( the driving force) pushes at a frequency which is equal to the resonant frequency of the swing

Question 24

What can be used to decrease the effect of resonance

Answer 24

Damping

Question 25

What is the relationship between degree of damping and resonant frequency

Answer 25

As the degree of damping increases, the resonant frequency decreases

Question 26

How does amplitude change on a graph when damped at resonant frequency

Answer 26

Peak moves to the left, decreases in height and becomes wider/more flat

Question 27

Define damping

Answer 27

The force opposes motion

Question 28

What is meant by forced vibrations

Answer 28

When periodic driving force is applied Frequency depends on frequency of driving force

Question 29

What is always true when a damping force acts on a vibrating system

Answer 29

Force acts in the opposite direction to the velocity

Question 30

Discuss the motions of a ball moving in circular motion with reference to newtons laws (part 1 of question)

Answer 30

1st law: ball doesn’t travel in a straight line, so there must be a force acting on it. Direction is changing, so velocity is changing, so object is accelerating 2nd law: force on the ball causes it to accelerate in the same direction as the force. The force is centripetal, so acts towards centre of circle 3rd law: the ball pulls on the central point of support with force equal and opposite to force pulling on ball from the centre. The direction of the force exerted by the ball acts outwards

Question 31

Explain why, for a ball moving with circular motion, in practice the string wont be horizontal

Answer 31

There is no resultant force in the vertical direction There are 2 components of force, as horizontal provides the centripetal force and the vertical force (tension) supports the weight of the ball.