CIE May 2020 9709 Mechanics Paper 41

CIE May 2020 9709 Mechanics Paper 41 (pdf)

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1. Three coplanar forces of magnitudes 100 N, 50 N and 50 N act at a point A, as shown in the diagram. The value of cos α is 4/5.
   Find the magnitude of the resultant of the three forces and state its direction
2. A car of mass 1800 kg is towing a trailer of mass 400 kg along a straight horizontal road. The car and trailer are connected by a light rigid tow-bar. The car is accelerating at 1.5 m s⁻². There are constant resistance forces of 250 N on the car and 100 N on the trailer.
   (a) Find the tension in the tow-bar
   (b) Find the power of the engine of the car at the instant when the speed is 20 m s⁻¹
3. A particle P is projected vertically upwards with speed 5 m s⁻¹ from a point A which is 2.8 m above horizontal ground.
   (a) Find the greatest height above the ground reached by P.
   (b) Find the length of time for which P is at a height of more than 3.6 m above the ground
4. The diagram shows a ring of mass 0.1 kg threaded on a fixed horizontal rod. The rod is rough and the coefficient of friction between the ring and the rod is 0.8. A force of magnitude T N acts on the ring in a direction at 30° to the rod, downwards in the vertical plane containing the rod. Initially the ring is at rest.
   (a) Find the greatest value of T for which the ring remains at rest
   (b) Find the acceleration of the ring when T = 3.

5. A child of mass 35 kg is swinging on a rope. The child is modelled as a particle P and the rope is modelled as a light inextensible string of length 4 m. Initially P is held at an angle of 45Å to the vertical (see diagram).
   (a) Given that there is no resistance force, find the speed of P when it has travelled half way along the circular arc from its initial position to its lowest point.
   (b) It is given instead that there is a resistance force. The work done against the resistance force as P travels from its initial position to its lowest point is X J. The speed of P at its lowest point is 4 m s⁻¹.
   Find X.
6. A particle moves in a straight line AB. The velocity vm s⁻¹ of the particle ts after leaving A is given by v = k(t² − 10t + 21), where k is a constant. The displacement of the particle from A, in the direction towards B, is 2.85 m when t = 3 and is 2.4 m when t = 6.
   (a) Find the value of k. Hence find an expression, in terms of t, for the displacement of the particle from A
   (b) Find the displacement of the particle from A when its velocity is a minimum
7. A particle P of mass 0.3 kg, lying on a smooth plane inclined at 30° to the horizontal, is released from rest. P slides down the plane for a distance of 2.5 m and then reaches a horizontal plane. There is no change in speed when P reaches the horizontal plane. A particle Q of mass 0.2 kg lies at rest on the horizontal plane 1.5 m from the end of the inclined plane (see diagram). P collides directly with Q.
   (a) It is given that the horizontal plane is smooth and that, after the collision, P continues moving in the same direction, with speed 2 m s⁻¹.
   Find the speed of Q after the collision
   (b) It is given instead that the horizontal plane is rough and that when P and Q collide, they coalesce and move with speed 1.2 m s⁻¹.
   Find the coefficient of friction between P and the horizontal plane

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