CIE Oct 2021 9709 Mechanics Paper 41

CIE Oct 2021 9709 Mechanics Paper 41 (pdf)

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1. A bus moves from rest with constant acceleration for 12 s. It then moves with constant speed for 30 s before decelerating uniformly to rest in a further 6 s. The total distance travelled is 585 m
   (a) Find the constant speed of the bus.
   (b) Find the magnitude of the deceleration
2. Two small smooth spheres A and B, of equal radii and of masses km kg and m kg respectively, where k > 1, are free to move on a smooth horizontal plane. A is moving towards B with speed 6 m s⁻¹ and B is moving towards A with speed 2 m s⁻¹. After the collision A and B coalesce and move with speed 4 m s⁻¹.
   (a) Find k.
   (b) Find, in terms of m, the loss of kinetic energy due to the collision.
3. Coplanar forces of magnitudes 24 N, P N, 20 N and 36 N act at a point in the directions shown in the diagram. The system is in equilibrium.
   Given that sin α = 3/5, find the values of P and θ
4. A particle of mass 12 kg is stationary on a rough plane inclined at an angle of 25° to the horizontal. A force of magnitude P N acting parallel to a line of greatest slope of the plane is used to prevent the particle sliding down the plane. The coefficient of friction between the particle and the plane is 0.35.
   (a) Draw a sketch showing the forces acting on the particle.
   (b) Find the least possible value of P.

5. A car of mass 1600 kg travels at constant speed 20 m s⁻¹ up a straight road inclined at an angle of sin⁻¹ 0.12 to the horizontal.
   (a) Find the change in potential energy of the car in 30 s
   (b) Given that the total work done by the engine of the car in this time is 1960 kJ, find the constant force resisting the motion.
   (c) Calculate, in kW, the power developed by the engine of the car.
   (d) Given that this power is suddenly decreased by 15%, find the instantaneous deceleration of the car.
6. A particle P moves in a straight line starting from a point O and comes to rest 14 s later. At time ts after leaving O, the velocity v m s⁻¹ of P is given by
7. Two particles A and B of masses 2 kg and 3 kg respectively are connected by a light inextensible string. Particle B is on a smooth fixed plane which is at an angle of 18° to horizontal ground. The string passes over a fixed smooth pulley at the top of the plane. Particle A hangs vertically below the pulley and is 0.45 m above the ground (see diagram). The system is released from rest with the string taut. When A reaches the ground, the string breaks.
   Find the total distance travelled by B before coming to instantaneous rest. You may assume that B does not reach the pulley.

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