CIE March 2020 9709 Mechanics Paper 42

CIE March 2020 9709 Mechanics Paper 42 (pdf)

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1. A lorry of mass 16 000 kg is travelling along a straight horizontal road. The engine of the lorry is working at constant power. The work done by the driving force in 10 s is 750 000 J.
   (a) Find the power of the lorry’s engine
   (b) There is a constant resistance force acting on the lorry of magnitude 2400 N.
   Find the acceleration of the lorry at an instant when its speed is 25 m s⁻¹.
2. A particle P of mass 0.4 kg is on a rough horizontal floor. The coefficient of friction between P and the floor is μ. A force of magnitude 3 N is applied to P upwards at an angle α above the horizontal, where tan α = 3/4. The particle is initially at rest and accelerates at 2 m s⁻².
   (a) Find the time it takes for P to travel a distance of 1.44 m from its starting point.
   (b) Find μ.
3. The diagram shows the vertical cross-section of a surface. A, B and C are three points on the crosssection. The level of B is h m above the level of A. The level of C is 0.5 m below the level of A. A particle of mass 0.2 kg is projected up the slope from A with initial speed 5 m s⁻¹. The particle remains in contact with the surface as it travels from A to C.
   (a) Given that the particle reaches B with a speed of 3 m s⁻¹ and that there is no resistance force, find h.
   (b) It is given instead that there is a resistance force and that the particle does 3.1 J of work against the resistance force as it travels from A to C.
   Find the speed of the particle when it reaches C
4. A cyclist travels along a straight road with constant acceleration. He passes through points A, B and C. The cyclist takes 2 seconds to travel along each of the sections AB and BC and passes through B with speed 4.5 m s⁻¹. The distance AB is 4/5 of the distance BC.
   (a) Find the acceleration of the cyclist.
   (b) Find AC
5. Coplanar forces, of magnitudes F N, 3 N, 6 N and 4 N, act at a point P, as shown in the diagram.
   (a) Given that α = 60, and that the resultant of the four forces is in the direction of the 3 N force, find F
   (b) Given instead that the four forces are in equilibrium, find the values of F and α

6. On a straight horizontal test track, driverless vehicles (with no passengers) are being tested. A car of mass 1600 kg is towing a trailer of mass 700 kg along the track. The brakes are applied, resulting in a deceleration of 12 m s⁻². The braking force acts on the car only. In addition to the braking force there are constant resistance forces of 600 N on the car and of 200 N on the trailer.
   (a) Find the magnitude of the force in the tow-bar.
   (b) Find the braking force
   (c) At the instant when the brakes are applied, the car has speed 22 m s⁻¹. At this instant the car is 17.5 m away from a stationary van, which is directly in front of the car. Show that the car hits the van at a speed of 8 m s⁻²
   (d) After the collision, the van starts to move with speed 5 m s⁻¹ and the car and trailer continue moving in the same direction with speed 2 m s⁻¹.
   Find the mass of the van
7. A particle moves in a straight line through the point O. The displacement of the particle from O at time ts is s m, where
   (a) Find the value of t when the particle is instantaneously at rest during the first 6 seconds of its motion. At t = 6, the particle hits a barrier at a point P and rebounds.
   (b) Find the velocity with which the particle arrives at P and also the velocity with which the particle leaves P.
   (c) Find the total distance travelled by the particle in the first 10 seconds of its motion

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