CIE March 2022 9709 Mechanics Paper 42

CIE March 2022 9709 Mechanics Paper 42 (pdf)

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1. A crane is used to raise a block of mass 600 kg vertically upwards at a constant speed through a height of 15 m. There is a resistance to the motion of the block, which the crane does 10 000 J of work to overcome.
   (a) Find the total work done by the crane.
   (b) Given that the average power exerted by the crane is 12.5 kW, find the total time for which the block is in motion.
2. A particle P is projected vertically upwards from horizontal ground with speed um s⁻¹. P reaches a maximum height of 20 m above the ground.
   (a) Find the value of u.
   (b) Find the total time for which P is at least 15m above the ground.
3. A car of mass m kg is towing a trailer of mass 300 kg down a straight hill inclined at 3° to the horizontal at a constant speed. There are resistance forces on the car and on the trailer, and the total work done against the resistance forces in a distance of 50 m is 40 000 J. The engine of the car is doing no work and the tow-bar is light and rigid.
   (a) Find the value of m.
   The resistance force on the trailer is 200 N.
   (b) Find the tension in the tow-bar between the car and the trailer.

4. The total mass of a cyclist and her bicycle is 70 kg. The cyclist is riding with constant power of 180W up a straight hill inclined at an angle ! to the horizontal, where sin α = 0.05. At an instant when the cyclist’s speed is 6 m s⁻¹, her acceleration is −0.2m s⁻². There is a constant resistance to motion of magnitude F N.
   (a) Find the value of F.
   (b) Find the steady speed that the cyclist could maintain up the hill when working at this power.
5. Four coplanar forces act at a point. The magnitudes of the forces are 10 N, F N, GN and 2F N. The directions of the forces are as shown in the diagram.
   (a) Given that the forces are in equilibrium, find the values of F and G.
   (b) Given instead that F = 3, find the value of G for which the resultant of the forces is perpendicular to the 10 N force
6. A cyclist starts from rest at a fixed point O and moves in a straight line, before coming to rest k seconds later. The acceleration of the cyclist at time ts after leaving O is am s⁻².
   (a) Find the value of k
   (b) Find the maximum speed of the cyclist.
   (c) Find an expression for the displacement from O in terms of t. Hence find the total distance travelled by the cyclist from the time at which she reaches her maximum speed until she comes to rest.
7. A bead, A, of mass 0.1 kg is threaded on a long straight rigid wire which is inclined at

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