1. Further Mechanics

Question 1

How would you convert an angle from degrees to radians?

Answer 1

Angle in radians x 2pi/360

Question 2

What is the definition of angular speed?

Answer 2

The angle that an object rotates through per second

Question 3

What is meant by the period and frequency of rotation?

Answer 3

time taken for a complete rev. the number of complete rev.s per second.

Question 4

How would you calculate the angular speed of an object in circular motion using its frequency?

y.

Answer 4

=2pi f

Question 5

What is meant by centripetal acceleration and centripetal force?

Answer 5

If an object is moving in a circle, centripetal acceleration is the acceleration of the object directed towards the centre of the circle.

Centripetal force is the force towards the centre of the circle responsible for the centripetal acceleration.

Question 6

What is the definition of simple harmonic motion?

Answer 6

The oscillation of an object in which the object’s acceleration is directly proportional to its displacement from its equilibrium position, and the acceleration is always directed towards the equilibrium.

Question 7

What is meant by the frequency and period of an oscillation?

Answer 7

The frequency of oscillation is the number of complete cycles per second. The period of oscillation is the time taken for a complete cycle.

Question 8

What is the phase difference between the displacement and the velocity of an object moving with SHM?

Answer 8

The velocity is 12E radians ahead of the displacement.

Question 9

For an object undergoing simple harmonic motion, Does maximum velocity occur at equilibrium or maximum displacement ?

Answer 9

Equilibrium

Question 10

For an object undergoing simple harmonic motion, Does minimum velocity occur at equilibrium or maximum displacement?

Answer 10

Maximum displacement

Question 11

For an object undergoing simple harmonic motion, Does maximum acceleration occur at equilibrium or maximum displacement?

Answer 11

Maximum displacement

Question 12

For an object undergoing simple harmonic motion, Does minimum acceleration occur at equilibrium or maximum displacement?

Answer 12

Equilibrium

Question 13

Describe how the kinetic and potential energy of an object moving with SHM change with time.

Answer 13

At its maximum displacement, the object’s kinetic energy, Ex, is zero (so it has zero velocity). All of its energy is potential energy, E,. As the object moves towards the equilibrium position, the restoring force does work on the object and transfers some Er to Ex. At the equilibrium position, the object’s Er is said to be zero and its Ex is maximum — so its velocity is maximum. As the object moves away from the equilibrium, all that Ex is transferred back to E, again.

Question 14

Describe an experiment that you could do with a mass on a spring to investigate the relationship of the period of oscillation with the mass and spring constant.

Answer 14

Put a known mass into a trolley and attach a horizontal spring to one side of the trolley, where the other end of the spring is attached to a wall. Have a position sensor on the other side of the trolley to the spring — this position sensor measures the displacement of the mass. Set the mass oscillating and use the data logger and the computer to find the period of oscillation. Repeat the experiment, but vary the mass and spring constant and observe how the period changes.

Question 15

Describe an experiment you could do to verify the relationship of the period of oscillation of a pendulum with the pendulum length, mass and amplitude.

Answer 15

Set up a simple pendulum made of a bob at the end of a stiff rod.
Attach it to an angle sensor and computer, so the angle of the pendulum is recorded continuously as it oscillates and the period is calculated.

Vary the length and observe how the period changes.

Question 16

What is the difference between a free vibration and a forced vibration?

Answer 16

A free vibration involves no transfer of energy between the oscillating object and its surroundings. The object will continue to oscillate at its natural frequency and with the same amplitude forever. A forced vibration occurs if there’s a periodic external driving force acting on the object.

Question 17

Describe the phase difference between a driving oscillation and an oscillating object when the driving frequency is much lower than the natural frequency.

Answer 17

the driver displacement and oscillator displacement are in phase (the oscillator can easily ‘keep up’ with the driver).

Question 18

Describe the phase difference between a driving oscillation and an oscillating object when the driving frequency is equal to the natural frequency.

Answer 18

the driver displacement and oscillator displacement are 90° out of phase.

Question 19

Describe the phase difference between a driving oscillation and an oscillating object when the driving frequency is much higher than the natural frequency.

Answer 19

the driver and oscillator displacement will be completely out of phase.

Question 20

What is resonance, and when does it occur?

Answer 20

occurs when the driving frequency approaches the natural frequency of an object and the object begins to oscillate with a rapidly increasing amplitude.

Question 21

Give three examples of situations where resonance can occur.

Answer 21

E.g. any three from: a radio’s electric circuit resonating when it’s tuned to the same frequency as a radio station
/ a glass resonating when driven by a sound wave at its natural frequency
/ a column of air in an organ pipe resonating when driven by the motion of air at its base
/ a swing in a playground resonating when it’s pushed by someone at its natural frequency.

Question 22

What is meant by a damping force?

Answer 22

acts on an oscillator and causes it to lose energy to its surroundings, reducing the amplitude of its oscillations.

Question 23

Name and briefly describe the four types of damping.

Answer 23

Light damping — damping such that an oscillating system takes a long time to stop, and the amplitude of the system reduces by only a small amount each period.

Heavy damping — damping such that the system takes less time to stop oscillating than a lightly damped system, and the amplitude gets much smaller each period.

Critical damping — damping such that the amplitude of an oscillating system is reduced (and so the system returns to equilibrium) in the shortest possible time.

Overdamping — extremely heavy damping such that an oscillating system takes longer to return to equilibrium than a critically damped system.