Further Mechanics

Question 1

What is a cyclotron and how does it work?

Answer 1

A type of particle accelerator where particles start off in the centre of the accelerator, and electric and magnetic fields cause them to move in circles of increasing size

Question 2

If a car is moving in a circle, which was is its velocity and acceleration directed?

Answer 2

• Velocity directed at a tangent to the circle
• Acceleration directed towards the centre of the circle

Question 3

When a car is moving in a circle, what remains constant and what constantly changes?

Answer 3

• Magnitude of linear velocity remains constant
• Linear velocity constantly changes

Question 4

Define Centripetal Force

Answer 4

The collective name for any resultant force directed towards the centre of the circle which makes an object move in a circle, often gravity or friction

Question 5

Define simple harmonic motion

Answer 5

Acceleration is proportional to displacement in the opposite direction

Question 6

Define resonance

Answer 6

When the driving frequency matches the natural frequency in a system, there is a rapid increase in amplitude of the wave

Question 7

Define damping

Answer 7

The decrease in amplitude of a oscillating object over time , caused by energy lost as heat by friction

Question 8

Define free oscillation

Answer 8

An oscillation with no external, resultant driving force

Question 9

Define forced oscillation

Answer 9

An oscillation with an external, resultant driving force

Question 10

Define potential energy

Answer 10

Energy that is stored, such as elastic strain energy

Question 11

What are simple harmonic oscillators?

Answer 11

Systems which oscillate with simple harmonic motion

Question 12

Give the 2 common types of SHO

Answer 12

• Masses on springs
• Pendulums

Question 13

Describe how a mass on a spring works

Answer 13

• When the mass is pushed or pulled either side of the equilibrium position, there is a restoring force that is exerted on it.
• The size and direction of this force are given by Hooke’s Law.

Question 14

In a mass-spring system, what is the relationship that the time period squared has with: mass, spring constant and amplitude?

Answer 14

• Time period squared is proportional to the mass
• Time period squared is proportional to the inverse of the spring constant
• Time period is not affected by amplitude

Question 15

Derive the simple pendulum formula

Answer 15

• F = ma
• acceleration is component of weight in the direction of the bob’s motion, so F = mgsinθ
  -F = ma = -mgsinθ
• a = -gsinθ
• Arc length(s) = rθ, so θ = s/r where r = length of string(l)
• Small angle approximation so a = -gsinθ becomes a = -gθ
• a = -gs/l
• Centripetal acceleration: a = -ω²x = -(2πf)²x , so a/x = -(2πf)²
• -a/x = -a/s = (2πf)² = g/l
• T = 2π x √l/g

Question 16

In a simple pendulum, what is the relationship that the time period squared has with the: mass, length of string and amplitude

Answer 16

• Time period is not affected by mass
• Time period squared is proportional to the length of string
• Time period is not affected by amplitude

Question 17

How does a U-tube work?

Answer 17

• The U- shaped tube contains water which at equilibrium, is at the same level on either side.
• When water is pushed down on one side, the other side raises the same amount
• When the pressure is released, each side water levels rise and fall
• As the water oscillates, it will exchange kinetic energy and potential energy
• At the equilibrium position, the kinetic energy is at a maximum and the potential energy will be zero

Question 18

What is the equation for time period of a U-tube?

Answer 18

T = 2π x √L/2g

Question 19

State the U-tube equation

Answer 19

T = 2π√L/2g

Question 20

Define driving frequency

Answer 20

The frequency of a periodic external force which can force a system to vibrate

Question 21

Give 3 examples of resonance

Answer 21

• A radio being tuned so that the electric circuit resonates at the same frequency as the radio station
• Glass resonating when driven by a sound wave of the right frequency
• A swing resonates if it’s driven by someone pushing at its natural frequency

Question 22

What is a synonym for damping forces?

Answer 22

Dissipative forces

Question 23

Describe the difference between light and heavy damping

Answer 23

• Lightly damped systems take a long time to stop oscillating, and their amplitude reduces a small amount per period
• Heavily damped systems take less time to stop oscillating, and their amplitudes get reduce a greater amount per period

Question 24

Define critical damping

Answer 24

The amplitude is reduced in the shortest possible time

Question 25

Define Overdamping

Answer 25

Damping which takes longer to return to equilibrium than a critically damped system

Question 26

Describe the difference between the resonance peaks of light and heavy damping

Answer 26

• Light damping has sharp resonance peak
• Amplitude only increases dramatically when driving frequency is close to natural frequency
• Heavy damping has a flatter response
• Amplitude doesn’t increase much near the natural frequency and they aren’t as sensitive to the driving frequency

Question 27

What is the condition under which the equation for the simple harmonic motion for a simple pendulum applies?

Answer 27

Oscillations must be of small amplitude

Question 28

How do you calculate the number of oscillations needed for two pendulums with different time periods to be next in phase?

Answer 28

• Divide the smaller time period by the larger time period
• Multiply the answer by 100