MECHANICS COURSEWORK SPRING 2015 Hand-in deadline: Thursday, 16 April (11 pm) This coursework must be your own individual work. You should not confer with others. Work not put in the correct submission box by the deadline above will not be marked. No marks will be given if working is not shown. Take g = 9.81 m s–2. If you cannot do part of a question you should not spend excessive time on it. Question 1 (a) When struck, a golf ball of mass 0.045 kg is given an impulse of 1.6 N s. Find its initial speed. (b) The golf ball travels a horizontal distance of 120 m over flat ground before bouncing. Ignoring air resistance, find the two possible angles to the ground with which it could have been struck. (c) The ball strikes a wall 65 m beyond the first bounce. Assuming the smaller of the two angles in part (b), and a coefficient of restitution e = 0.6 between ball and ground, at what height does the ball hit the wall? wall 120 m 65 m Question 2 Two cars, A of mass 800 kg and B of mass 1200 kg, collide at a 90° crossroads as shown. The collision is completely inelastic and after the collision the cars continue to move as a single body, sliding a distance 18 m at angle 30º to the original direction of A before stopping. A 800 kg 18 m 30 m/s 30o (a) If car A was travelling at 30 m s–1 before the collision, find the speed of car B before the collision and the speed of the combined vehicles after the collision. (b) Assuming that all car wheels lock at the point of impact, find the total coefficient of kinetic friction between the tyres and the ground. Page 1 B 1200 kg MECHANICS COURSEWORK SPRING 2015 Question 3 Four uniform rods, each of mass m and length L, are freely jointed at A, B, C, D and hang from A as shown. Points A and C are connected by a spring of stiffness k = 3mg/L and unstretched length L. AB makes angle θ with the vertical. (a) Show that the potential energy of the system is given by: V mgL 6 cos 2 θ 10 cos θ constant (b) Show that there are two positions of equilibrium and determine their stability. A L L k=3mg/L B L L C Page 2 D

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