QUESTION 1 SECTION A (a) Derive an expression for the tension in the cable supporting a lift when (i) it is going up, and (ii) it is coming down. An elevator of gross kg starts moving upwards with a constant acceleration, and acquires a velocity of 2 m/s. after travelling a distance of 3 m. Find the pull in the cables during the accelerated motion. If the elevator, when stopping moves with a constant deceleration from a constant velocity of 2 m/s and comes to rest in 2 s. calculate the force transmitted by a man of mass 75 kg to the floor during (15 mks) stoppage. (b) State the D'Alembert's principle. A body of mass 10 kg is moving over a smooth surface, whose equation of motion is given by the relation, S-2512-71+8 where (s) is in metres and (t) in seconds. Find the magnitude of force responsible for the motion after 10 seconds. Is the body accelerating or decelerating? (10 mks) QUESTION 2 a) A cage descends in a mine shaft with an acceleration of 0.5 m/s². After the cage has travelled 25 m, a stone is dropped from the top of the shaft. Determine the (i) time taken by the stone to hit the cage, and (ii) distance travelled by the cage before impact. (13 mks) b) A truck is moving downward inclined at 10° when the driver applies brakes, with the result that the truck decelerates at a steady rate of 1 m/s². Investigate whether a 500 kg mass placed on the truck will slide or remain stationary relative to the truck. Assume the coefficient of friction between the truck surface and the road as 0.4. What will be the factor of safety against slipping for this load? (12 mks) QUESTION 3 (a) (i) Mention the types of plane motions that may occur in a rigid body. In a crank and connecting rod mechanism, the crank is 300 mm long and the connecting rod 1200 mm long. If the crank rotates uniformly at 1800 r.p.m., use the analytical method to find the velocity of the cross head when the crank is inclined at 45° with the inner dead centre. (15 mks) (b) Length of crank AB is 1000 mm and that of connecting rod is 225mm. The crank is at 360 r.p.m. Find the velocity of cross head, when the crank has turned 30° with line joining the centres. (10 mks) SECTION B QUESTION 4 a) Using simple sketch and energy equations, show the state of energy for a body of water at rest on a mountain-cliff. (5 mks) b) If the water with a mass m, falls from a height h, into a running stream down below, compare the state of energy of the water at the mountain-cliff, midway down the cliff and in the stream. c) From your observation, state a theorem for the energy behavior. d) If the mountain height is 2 km, calculate the velocity with which the water flows into the stream (12 mks) (3 mks) below? (5 mks) RF 773 and Somester 2012 QUESTION 5 In an experimental analysis, the following data were generated for a frictionless body moving on a level surface. Force (N) Distance moved (mm) 0 ° 2 2 4 3 6 8 5 10 5 20 5 30 Graphically represent the energy behavior using a force-distance graph (6 mks). ii) iii) How will you describe the force acting on the body based on the graph generated? (6 mks) Using the graph, estimate the total work done by the body (7 mks). iv) Assuming the force to be a spring force, estimate the spring constant from the graph generated (6 mks). QUESTION 6 a) A car weighing 5000 kg with an engine efficiency of 0.75 had a piston force of 1000 N. Moving from rest, the car attained a speed of 60 km/h in 20 minutes: i. How much power will be delivered to the propeller shaft (6 mks) ii. Determine the maximum power developed by the engine (6 mks) iii. How much power is lost by the engine (4 mks) iv. Give the main causes of power loss (4 mks) V. Using the work concept, prove that power is a product of force and velocity (5mks)