CIE Oct 2020 9709 Mechanics Paper 42

CIE Oct 2020 9709 Mechanics Paper 42 (pdf)

• Show Step-by-Step Solutions

1. Two particles P and Q, of masses 0.2 kg and 0.5 kg respectively, are at rest on a smooth horizontal plane. P is projected towards Q with speed 2 m s⁻¹.
   (a) Write down the momentum of P
   (b) After the collision P continues to move in the same direction with speed 0.3 m s⁻¹. Find the speed of Q after the collision.
2. A car of mass 1800 kg is travelling along a straight horizontal road. The power of the car’s engine is constant. There is a constant resistance to motion of 650 N.
   (a) Find the power of the car’s engine, given that the car’s acceleration is 0.5 m s⁻² when its speed is 20 m s⁻¹.
   (b) Find the steady speed which the car can maintain with the engine working at this power.
3. A block of mass m kg is held in equilibrium below a horizontal ceiling by two strings, as shown in the diagram. One of the strings is inclined at 45° to the horizontal and the tension in this string is T N. The other string is inclined at 60° to the horizontal and the tension in this string is 20 N. Find T and m.
4. The diagram shows a velocity-time graph which models the motion of a car. The graph consists of four straight line segments. The car accelerates at a constant rate of 2 m s⁻² from rest to a speed of 20 m s⁻¹ over a period of T s. It then decelerates at a constant rate for 5 seconds before travelling at a constant speed of V m s⁻¹ for 27.5 s. The car then decelerates to rest at a constant rate over a period of 5 s.
   (a) Find T
   (b) Given that the distance travelled up to the point at which the car begins to move with constant speed is one third of the total distance travelled, find V

5. A particle is projected vertically upwards with speed 40 m s⁻¹ alongside a building of height h m.
   (a) Given that the particle is above the level of the top of the building for 4 s, find h.
   (b) One second after the first particle is projected, a second particle is projected vertically upwards from the top of the building with speed 20 m s⁻¹. Denoting the time after projection of the first particle by t s, find the value of t for which the two particles are at the same height above the ground.
6. A block of mass 5 kg is placed on a plane inclined at 30° to the horizontal. The coefficient of friction between the block and the plane is μ.
   (a) When a force of magnitude 40 N is applied to the block, acting up the plane parallel to a line of greatest slope, the block begins to slide up the plane (see Fig. 6.1). Show that μ < 1/5 √3
   (b) When a force of magnitude 40 N is applied horizontally, in a vertical plane containing a line of greatest slope, the block does not move (see Fig. 6.2). Show that, correct to 3 decimal places, the least possible value of μ is 0.152.
7. A particle P moves in a straight line, starting from a point O with velocity 1.72 m s⁻¹. The acceleration a m s⁻² of the particle, ts after leaving O, is given by a = 0.1t^3/2
   (a) Find the value of t when the velocity of P is 3 m s⁻¹
   (b) Find the displacement of P from O when t = 2, giving your answer correct to 2 decimal places
8. Two particles A and B, of masses 0.3 kg and 0.5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to a horizontal plane and to the top of an inclined plane. The particles are initially at rest with A on the horizontal plane and B on the inclined plane, which makes an angle of 30° with the horizontal. The string is taut and B can move on a line of greatest slope of the inclined plane. A force of magnitude 3.5 N is applied to B acting down the plane (see diagram).
   (a) Given that both planes are smooth, find the tension in the string and the acceleration of B.
   (b) It is given instead that the two planes are rough. When each particle has moved a distance of 0.6 m from rest, the total amount of work done against friction is 1.1 J. Use an energy method to find the speed of B when it has moved this distance down the plane. [You should assume that the string is sufficiently long so that A does not hit the pulley when it moves 0.6 m.]

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.