OCT Half-term H/W 2013

1. A boy swings a mass on a string in a horizontal circle at 120 revolutions per minute. The length of the string is 75cm and the mass is 50g.

(a) Calculate the tension in the string.

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(b) He now swings the mass at the same rate in a vertical circle.

(i) Using a diagram, explain how the tension in the string varies throughout the motion.

[4](ii) Calculate the maximum and minimum values of the tension.

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Total 10 marks

2. An object of mass 2kg is rotated in a vertical circle on a cord of length 1m. The cord will breakwhen the tension in it becomes 500N. The speed of rotation is gradually increased from zero.(a) Find the angular velocity at which the string breaks..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

[4](b) Draw a diagram to show the position at which the string breaks and the subsequent

motion of the object.[4]

Total 8 marks

3. (a) Explain how a body with a constant speed can have centripetal acceleration

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(b) (i) In a question about a spacecraft in orbit, a student writes:“The gravitational pull of the Earth is balanced by the centripetal force of the space craft and so it stays in orbit.”Explain why this statement and is incorrect and write a corrected version

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[4](ii) Use your answer to (b)(i) to explain why an astronaut inside the spacecraft experiences

weightlessness.

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Total 11 marks

Motion in a circle

1 Calculate the angular velocity (i) in degrees (ii) in radians ofa) a fan blade rotating at 2.5 r.p.m.

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the minute hand of a clock……………………………………………………

2 All points on the Earth rotate with an angular velocity of 7.3 x 10-5 rad s-1. What is the speed of a point on the equator? Take the radius of the Earth to be 6.4 x 103km.

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3 A helicopter blade is designed to rotate at such an angular velocity that the tip of the rotor blade is less than the speed of sound in air, which is 340 m s-1. The blades rotate at 260 r.p.m. Calculate the maximum possible length of the blades.

4 A compact disc (CD) player varies the rate of rotation of the disc in order to keep the track from which the music is being reproduced moving at a constant linear speed of 1.30 m s-1. Calculate the rates of rotation of a 12.0 cm disc when the music is being read from:a) the outer edge of the disc.b) A point 2.55 cm from the centre of the disc.Give your answers in rad s-1 and rev min-1

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January 2004

January 2004

January 2005

3. The graph below shows how the momentum of this lorry varies over the first Minute.

8 0

6 0

4 0

2 0

01 0 2 0 3 0 40 5 0 6 0

t /s

M o m en tu m /1 0 N s4

Define momentum.

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State the physical quantity represented by the slope of this graph.

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Determine the magnitude of this quantity at t = 20 s.

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Explain the shape of this graph.

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(Total 7 marks)

5. The picture shows a toy with two plastic spheres, each suspended by plastic rods. Each sphere is able to swing freely in a vertical circle.

A student decides to carry out an experiment with the toy to investigate momentum. He allows one sphere to strike the other, and measures their speeds just before and just after the collision.

The table shows his data for one collision.

mass of sphere 1 54.0 g

mass of sphere 2 29.0 g

speed of sphere 1before collision

2.57 m s–1

speed of sphere 2before collision

0

speed of sphere 2after collision

2.12 m s–1

1

2

P iv o t

P las tic ro d s

S p h ere

Show that the speed of sphere 1 just after the collision is about 1.4 m s–l. Assume that the mass of each rod is negligible.

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Determine whether this is an elastic collision or an inelastic collision.

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In another experiment the student uses the toy to investigate motion in a vertical circle. He times sphere 2 (mass 29 g) as it swings around a complete vertical circle of radius 17 cm. This takes 0.37 s.

Calculate the average speed of the sphere.

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Speed = .....................................................(2)

Assuming that the sphere travels at this speed throughout its circular path,

(i) calculate the centripetal force acting on it while it is in motion

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Centripetal force = .....................................................(2)

(ii) calculate the net force exerted by the rods on the sphere when it is at the top of the circle.

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Tension = .....................................................(2)

(Total 12 marks)