CAIE Mathematics (9709)

A railway locomotive of mass 240 000 kg is towing a coach of mass 36 000 kg down a hill inclined at an angle of .sin004 to the horizontal. The driving force produced by the locomotive is 450 000 N and there are resistances to motion of 120 000 N on the locomotive and 15 000 N on the coach. The coupling between the locomotive and the coach is light, rigid and parallel to the hill. Find the acceleration of the locomotive and the tension in the coupling.

A car of mass 1400 kg travelling on a straight horizontal road accelerates uniformly from a speed of m15s to m02s over a distance of 175 m.

Find the time taken to travel the 175 m. [2] There is a constant resistance force of 800 N to the motion of the car .

(i) Use an ener gy method throughout to find the average power of the car 's engine as the speed increases from m15s to .m20s

Find the steady speed that the car could maintain on the horizontal road if the engine is working at the power found in (b)(i).

A particle P of mass 0.1 kg is projected vertically upwards with speed m30s from horizontal ground. At the same instant a particle Q of mass 0.4 kg is projected vertically upwards with speed m10s from a height of 15 m above the ground. P and Q move in the same vertical line.

Find the height above the ground at which P and Q collide. [4] When P and Q collide, they coalesce.

Find the speed of the combined particle at the instant that it reaches the ground. [5] 10°35° 5 kg 20 N A block of mass 5 kg is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude 20 N. The plane is inclined at an angle of 10° to the horizontal and the 20 N force acts at an angle of 35° above the line of greatest slope of the plane (see diagram). The coefficient of friction between the block and the plane is 0.4. The speed of the block when it passes a point O is .m2s Find the speed of the block when it has moved 3 m down the plane from O.

A particle starts from rest at a point O. The acceleration of the particle at time t s after leaving O is ,mas where ()at21 1 =+ - for t0H. Find the distance that the particle travels from O until the time at which its acceleration is zero. [8] 30°45°20° 15 N 25 N 30 N 20 NS N Four coplanar forces of magnitudes 20 N, 30 N, 15 N and 25 N act at a point P in the directions shown in Fig. 7.1. The forces act in a vertical plane. The resultant of these forces has magnitude S N and acts at an angle °a below the horizontal as shown in Fig. 7.2.

Find the value of S and the value of a. [6] A small ring of mass 0.6 kg is threaded on a rough straight horizontal wire. The four forces shown in Fig. 7.1 act on the ring and are in the same vertical plane as the wire. The ring starts from rest and takes 3 s to travel a distance of 2 m along the wire.

Find the coefficient of friction between the ring and the wire. [5] Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown. Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable ef fort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. * 0000800000012 *