(b) An elevator of mass 2 tonnes is to be lifted and lowered by means of a rope. Find the tension in the rope, when the elevator is moving: (i) upward with an acceleration of 2 m/s² and (ii) downward with an acceleration of 1.5 m/s². (10 mks) QUESTION 2 (a) A particle P is moving along the line OX with an acceleration of (61-18) ms² at time seconds. When 0 the displacement of P from O is zero and its speed is 24ms" in the direction OX. (i) Find the values of from which v 0 and the values of x for the computed values of r. (ii) Find the distance traveled in the first 3 seconds. (15 mks) (b) The relation between the angle of rotation (0 in radians and time (t) in seconds of rotating body is given by the equation: 0=2r²+3r²+10 Find displacement, angular velocity and angular acceleration after 4 seconds. (10 mks) QUESTION 3 (a) (i) Enumerate five (5) applications of kinematics in our day to day life. (5 mks) (ii) In a crank and connecting rod mechanism, the crank is 300 mm long and the connecting rod 1500 mm long. If the crank rotates uniformly at 300 r.p.m., use the analytical method to find the velocity of the cross head when the crank is inclined at 30° with the inner dead centre. (10 mks) (b) Length of crank AB is 100mm and that of connecting rod is 250mm. If the crank is rotating in clockwise direction at 1500 r.p.m. for the stated position, determine the angular velocity of the connecting rod and the velocity of the piston. (10 mks) 1 SECTION I QUESTION 4 (a) A wagon of mass 50 tonnes, starts from rest and travels 30 metres down a 1% grade and strikes a post with bumper spring. T If the rolling resistance of the track is 50 Ntonnes, find the velocity with which the wagon strikes the post. Also find the amount by which the spring will be compressed, if the bumper spring compresses Imm per 20 kN force. (10 mks) (b) (i) State the principle of conservation of energy and give example of devices or systems where the principle is confirmed. (5 mks) (ii) A hammer of mass 0.5 kg hits a nail of 25 g with a velocity of 5 m/s and drives it into a fixed wooden block by 25 mm. Find the resistance exhibited by the wooden block. (5 mks) QUESTION 5 (a) (i) Define the term Coefficient of Restitution (e). (5 mks) (ii) A mass of 300kg is allowed to fall vertically through 1 metre on to the top of a pile of mass 500kg. Assume that the falling mass and pile remain in contact after impact and that the pile is moved 150mm at each blow. Find, allowing for the action of gravity after impact: (1) The energy lost in the blow, and (2) the average resistance against the pile. members. (10mks) (b) A sphere of mass 1kg, moving at 3m/s, overtakes another sphere of mass 5kg moving in the same line at 60cm. Find the loss of K.E. during impact and show that the direction of motion of the first sphere is reversed. Take Coefficient of restitution as 0.75. (10 mks) QUESTION 6 (a) (i) Briefly explain the meaning of S.H.M and give two examples of its areas of application. (5 mks) (ii) A particle moving with simple harmonic motion performs 15 complete oscillations per minute and its speed when at a distance of 75 mm from the centre of oscillation is 5/7 of the maximum speed. Find the amplitude, the maximum acceleration and speed of the particle, when it is 55 mm from the centre of the oscillation. (10 mks) (b) A part of a machine of mass 8.5 kg has a reciprocating motion which is simple harmonic in character. It makes 265 complete oscillations in 1 minute. Find: (i) the accelerating force upon it and its velocity when it is 75 mm, from mid-stroke; (ii) the maximum accelerating force, and (iii). the maximum velocity if its total stroke its 225 mm, that is, if the amplitude of vibration is 112.2 mm. (10 mks)