CIE May 2022 9709 Mechanics Paper 43

CIE May 2022 9709 Mechanics Paper 43 (pdf)

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1. Two particles P and Q, of masses 0.3 kg and 0.2 kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 m s⁻¹ directly towards Q. After P and Q collide, Q begins to move with a speed of 3 m s⁻¹. (a) Find the speed of P after the collision
2. A particle P is projected vertically upwards from horizontal ground. P reaches a maximum height of 45 m. After reaching the ground, P comes to rest without rebounding. (a) Find the speed at which P was projected.
3. The displacement of a particle moving in a straight line is s metres at time t seconds after leaving a fixed point O. The particle starts from rest and passes through points P, Q and R, at times t = 5, t = 10 and t = 15 respectively, and returns to O at time t = 20. The distances OP, OQ and OR are 50 m, 150 m and 200 m respectively. The diagram shows a displacement-time graph which models the motion of the particle from t = 0 to t = 20. The graph consists of two curved segments AB and CD and two straight line segments BC and DE.
4. The diagram shows a block of mass 10 kg suspended below a horizontal ceiling by two strings AC and BC, of lengths 0.8m and 0.6 m respectively, attached to fixed points on the ceiling. Angle ACB = 90°. There is a horizontal force of magnitude F N acting on the block. The block is in equilibrium. (a) In the case where F = 20, find the tensions in each of the strings. (b) Find the greatest value of F for which the block remains in equilibrium in the position shown.

5. A cyclist is riding along a straight horizontal road. The total mass of the cyclist and her bicycle is 70 kg. At an instant when the cyclist’s speed is 4 m s⁻¹, her acceleration is 0.3 m s⁻². There is a constant resistance to motion of magnitude 30 N. (a) Find the power developed by the cyclist. The cyclist comes to the top of a hill inclined at 5° to the horizontal. The cyclist stops pedalling and freewheels down the hill (so that the cyclist is no longer supplying any power). The magnitude of the resistance force remains at 30 N. Over a distance of d m, the speed of the cyclist increases from 6 m s⁻¹ to 12 m s⁻¹. (b) Find the change in kinetic energy. (c) Use an energy method to find d.
6. Two particles P and Q, of masses 0.3 kg and 0.2 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley at B which is attached to two inclined planes. P lies on a smooth plane AB which is inclined at 60° to the horizontal. Q lies on a plane BC which is inclined at 30° to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes (see diagram). (a) It is given that the plane BC is smooth and that the particles are released from rest. Find the tension in the string and the magnitude of the acceleration of the particles. (b) It is given instead that the plane BC is rough. A force of magnitude 3 N is applied to Q directly up the plane along a line of greatest slope of the plane. Find the least value of the coefficient of friction between Q and the plane BC for which the particles remain at rest.
7. A particle P moves in a straight line through a point O. The velocity vm s⁻¹ of P, at time ts after passing O, is given by

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