6410

London
Examinations
GCE
Wednesday 4 June 1969 - 2nd Afternoon Session
Advanced Level/Advanced Supplementary
Mechanics M2
Time: 1 hour 30 minutes
Instructions to Candidates

Full marks may be obtained for answers to ALL questions. (Well, you can dream.)

In the boxes on the Answer Book, write your centre number, candidate number, the syllabus title (Mechanics), syllabus number (6410), paper number (M2), your surname and initials, signature, date, star sign and favourite pizza topping.

Whenever a numerical value of g is required, take g =9.8 ms-2.

Information for Candidates

A booklet 'Mathematical Formulae Including Pointless Numbers In The Back' is provided.

In calculations you are advised to show all the steps in your working, giving your answer at each stage.

This paper has 7 questions. Pages 5, 6, 7, 8 and 9 are blank, except for the bit in the middle which says "Blank Page". These pages have no purpose other than to speed the destruction of the rainforests.





edexcel P8034 R6410             3/3/3/3/6/12230
© 1997 Edexcel Foundation

This publication may only be reproduced in accordance with Edexcel Foundation copyright policy.
London Examinations is a division of Edexcel Foundation and is a trade mark of the University of London.
Edexcel Foundation is a Registered Charity.
Does anybody actually read this bit? Right, I'm off to the pub.

1. A car of mass 800 kg turns a corner which is banked at an angle a to the vertical, where sin a = 1/14. While travelling at a constant speed of 18ms-1, the car works at a rate of 1.2 kW. By considering the circular motion of the car, or otherwise, show that the car is a Lada.

(5 marks)

2. Particle A, of mass 4m kg, with a velocity vector (3i+8j) ms-1, collides in an inelastic collision with particle B, of mass 3m kg, which is initially at rest. The kinetic energy of B after the collision is 15m J, and the velocities of both particles after the collisions are in the same line as the initial velocity of particle A. By modelling particles A and B as a bus and a tram respectively, find the coefficient of restitution in the collision.

(7 marks)

3.

Look ma, a jumble of Greek letters!

Here is a jumble of Greek letters. Find µ.

(7 marks)

4.

Model on a catwalk. Walk like an Egyptian

A fashion show catwalk is inclined at an angle a from the horizontal, where tan a = 1/8. A supermodel walks down the catwalk with acceleration 0.3 ms-2. The coefficient of friction between the floor and the supermodel's platform shoes is 0.001. At time t seconds after the start of motion, the supermodel topples over, as shown in the diagram. By modelling the supermodel as a light rod, find the velocity at t seconds.

(9 marks)

5. Arshad and Barbara are trying to find the centre of mass of a non-uniform ruler of mass m. First, they suspend it from two inextensible strings, C and D, at a distance l and 3l from A respectively. It is found that the tension in D is 2/3 of the tension in C. Next, Barbara attaches a particle mass 3m to the ruler, such that this causes the two tensions to be equal.

Why?

(11 marks)

6. A lemming walks towards the edge of a cliff, 70m above sea level, with speed u. As it reaches the edge, it performs a backflip which changes the direction of its velocity, but keeps a constant magnitude. The lemming subsequently moves with projectile motion towards the sea.

Suggest a model for the lemming and find, in terms of u, the maximum distance from the sea that the lemming can reach.

(11 marks)

7.

Magnets. In a vertical circle. Aaarrghghh!

A magnet, modelled as a particle of mass m, is attached to an elastic string of natural length l and modulus 3mg/2l. The other end of the spring is fixed at a point O, and the spring is initially in equilibrium with the magnet vertically below O. The magnet is projected horizontally with a velocity u, and the system begins to describe a vertical circle. At an angle of 45° to the downward vertical, another magnet, of mass 2m, attaches to the magnet.

a) Show that the string becomes slack at an angle a from the upward vertical, where:
cos a = 4ml(u+1)2/3gu

b) State where in your answer you have used the assumptions:
i) Er... it must be something to do with energy, surely
ii) If I work backwards and fiddle the answer, the examiner won't notice

(50 marks)

END
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