Free Printable U6 - Revision for Mock

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U6 - Revision for Mock - Further Mechanics

Total questions: 26

Worksheet time: 1hrs 12mins

Name

Class

Date

A system is oscillating with simple harmonic motion. The energy of oscillation of the system doubles.

The amplitude of oscillation increases by a factor of

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

$\sqrt{2}$

A mass hanging from the end of a vertical spring is set into undamped simple harmonic

motion with amplitude A. The total energy of the oscillating system is E.

When the amplitude of oscillation is increased to 2A the total energy of the oscillating system becomes

4E²

A mass is hung from a spring and set into vertical oscillation.

The resultant force on the oscillating mass always acts

in the same direction as the velocity.

towards the equilibrium position.

vertically downwards.

vertically upwards.

Two systems are oscillating with simple harmonic motion. The angular frequency and amplitude of each oscillating system are summarised in the table.

The maximum acceleration of system 1 is a₁ and the maximum acceleration of system 2 is a₂.

Which statement is correct?

a₁= a₂ / 2

a₁ = a₂

a₁ = 2a₂

a₁ = 4a₂

The acceleration a of a simple harmonic oscillator is related to its displacement x by the equation

a = − 25 x.

What is the frequency of the oscillator?

0.80 Hz

1.3 Hz

4.0 Hz

5.0 Hz

Which one of the following gives the phase difference between the particle velocity and the particle displacement in simple harmonic motion?

$\frac{\pi}{4}$ rad

$\frac{\pi}{2}$ rad

$\frac{3\pi}{4}$ rad

$2\pi$ rad

An object oscillating in simple harmonic motion has a time period T. The first graph shows how its displacement varies with time. Which of the subsequent graphs, A to D, show how the kinetic energy, E_K, of the object varies with time?

A particle of mass 0.20 kg moves with simple harmonic motion of amplitude $2.0\times10^{-2}$ m. If the total energy of the particle is $4.0\times10^{-5}$ J, what is the time period of the motion?

$\frac{\pi}{4}$ seconds

$\frac{\pi}{2}$ seconds

$\pi$ seconds

$2\pi$ seconds

A pendulum of length l with a bob of mass m oscillates with frequency f.

What is the frequency of a pendulum of length 4l with a bob of mass 2m?

f/2

10.

The graph shows how the displacement of a simple harmonic oscillator varies with time.

Which of the following graphs shows how velocity varies with time for the same oscillator, over the same period?

11.

The graph shows how displacement varies with time for a particle moving with undamped simple harmonic motion during a particular time interval.

Which of the graphs represents the acceleration of the particle?

12.

The graph shows how displacement varies with time for a particle moving with undamped simple harmonic motion during a particular time interval.

Which of the graphs represents the total energy of the particle?

13.

A disc of diameter D is turning at a steady angular speed at frequency f about an axis through its centre.

What is the centripetal force on a small object O of mass m on the perimeter of the disc?

2πmfD

2πmf²D

2π²mf²D

2πmf²D²

14.

A particle, mass 0.020 kg, is moving with an angular velocity of 3π rad s^-1 around a circle of radius 0.50 m. The force, in N, responsible for this motion is

0.03π towards the centre of the circle

0.03π away from the centre of the circle

0.09π² towards the centre of the circle

0.09π² away from the centre of the circle

15.

A car, mass m, drives over a circular hump-back bridge of radius r with a constant speed v.

When it is at the top of the bridge, the force on the car from the bridge is given by

mg

$\frac{mv^2}{r}\ +\ mg$

$\frac{mv^2}{r}\ -\ mg$

$mg\ -\ \frac{mv^2}{r}$

16.

The diagram shows a disc of diameter 120mm that can turn about an axis through its centre.

The disc is turned through an angle of 30° in 20 ms. What is the average speed of a point on the edge of the disc during this time?

0.5π m s^-1

π m s^-1

1.5π m s^-1

2π m s^-1

17.

A ball of mass m, which is fixed to the end of a light string of length l, is released from rest at X. It swings in a circular path, passing through the lowest point Y at speed v.

If the tension in the string at Y is T, which one of the following equations represents a correct application of Newton’s laws of motion to the ball at Y?

T=\frac{mv^2}{l}-mg

$mg-T=\frac{mv^2}{l}$

$T-mg=\frac{mv^2}{l}$

$T+\frac{mv^2}{l}=mg$

18.

During the spin cycle of a washing machine, the clothes stick to the outer wall of the drum.

The drum spins at a rate of 1800 revolutions per minute. The radius of the drum is 36 cm. What is the magnitude and direction of centripetal acceleration of the clothes which are located on the wall of the barrel?

4.6 x 10⁷ m s^-2 towards the centre of the drum

4.6 x 10⁷ m s^-2 away from the centre of the drum

1.28 x 10⁴ m s^-2 towards the centre of the drum

1.28 x 10⁴ m s^-2 away from the centre of the drum

19.

A car is making a turn at speed v. The radius of the turn is r and the centripetal force on the car is F. If the car rounds the same curve at speed 2v, the required centripetal force is

F/2

20.

Four particles have the following masses (in terms of m), speeds (in terms of v), and radii (in terms of r). Which two particles have the same centripetal force? (Remember to select TWO options!)

Particle 1

Particle 2

Particle 3

Particle 4

21.

A particle travels at a constant speed around a circle of radius r with centripetal acceleration a. What is the time taken for ten complete rotations?

$\frac{\pi}{5}\sqrt{\frac{a}{r}}$

$\frac{\pi}{5}\sqrt{\frac{r}{a}}$

$20\pi\sqrt{\frac{a}{r}}$

$20\pi\sqrt{\frac{r}{a}}$

22.

A toy aeroplane makes 14 full revolutions in 6s. Which of the following gives the angular velocity of the toy aeroplane in rad s^-1?

$\frac{14\times\pi}{6}$

$\frac{14\times2\pi}{6}$

$\frac{6\times\pi}{14}$

$\frac{6\times2\pi}{14}$

23.

The mass rotates along a circular path, as indicated by the dotted line. The diameter of the circular path is 0.80 m and the period of rotation is 0.60 s.

Which of the following shows how the angular velocity can be determined?

$2\pi\times0.60$

$2\pi\div0.60$

$2\pi\times0.40\div0.60$

$2\pi\times0.40\times0.60$

24.

The plan view of a model racing car track is shown. Friction acts between a model racing car and the track. A car is moving round the track with a constant speed and reaches point P. Arrows indicating directions North and South are also shown.

The car then slides off the track at P.

Which of the following is the reason why the car slides off the track?

The centripetal force is acting in the N direction.

The centripetal force is acting in the S direction.

The frictional force is equal to the centripetal force.

The frictional force is not large enough.

25.

A small body of mass m rests on a horizontal turntable at a distance r from the centre.

If the maximum frictional force between the body and the turntable is mg/2, what is the angular speed at which the body starts to slip?

$\sqrt[]{\frac{gr}{2}}$

$\frac{g}{r}$

$\sqrt[]{\frac{g}{2r}}$

$\frac{1}{2}\sqrt[]{\frac{g}{r}}$

26.

A model aeroplane is moving at a constant speed, in a horizontal circle.

F and G are two positions of the model aeroplane. The velocity at F is v_F and the velocity at G is v_G, as shown.

As the model aeroplane moves from F to G, the change in velocity is Δv.

Which of the following is a correct vector diagram for this situation?

100 %

U6 - Revision for Mock - Further Mechanics

Total questions: 26

Worksheet time: 1hrs 12mins

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