week_8 - Week 8-Pr0blems 8-1 Two objects have masses of M...

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Unformatted text preview: Week 8-Pr0blems 8-1 Two objects have masses of M and 3M, respectively. If both have the same kinetic energy, which one has the larger linear momentum and by what factor? Why? 8-2 If the objects of problems 8—1 have the same linear momentum (magnitude), which will have the larger kinetic energy and by what factor? Why? 8—3 In order to conserve the total vector momentum of a many partic1e system, why is it necessary to have the external force equal to zero? [In all problems 8 »— 4 through 8 — 15 assume that Ex, = OJ 8-4 What is the difference between a totally elastic and a totally inelastic two body collision? 8—5 Show that in a totally elastic head on collision the relative velocity reverses during the collision, that is, relatively velocity after is negative of the relative velocity before the collision? 8-6 You drop a ball of mass 1kg from a height of 2m. The collision with Earth lasts for about 104 seconds and on bouncing the ball rises to a height of 1,.5m. is this collision totally elastic? Justify your answer. 8~7 When two objects of mass M1 and M2 with velocities V1 and V2 have a totally elastic head—on collision, the velocities after collision are given by: /= M V +% —‘» M1+M2 J M1+M2 V2“: ———M2 ’M' V2 +————2M‘K" —~> M| +M2 ~ M1+M2 Use these formulae to calculate to calculate V/ and V2/ for the following cases. i) M1=M2, V] =5m/SJ’5, V2=0 -—v ii) Ml << M2 (collision with a wall), VI = iom/sae, 1/2 = 0 ——> iii) M1 >> M2 (small object at rest, large object hits it), Vl 2: lOm/s 5c , V2 = 0 iv) Mi = 10kg M2: 5kg V1 =2m/SJE V2=—4m/s£ ———v 8-8 An object of mass M is sitting at rest when it is hit by another object of mass M traveling at V1 . The collision is glancing and totally elastic. What is the relationship between their velocity V1 / and V2/ after the collision? 8—9 An object of mass 5kg traveling at 4m/s a? collides with an object of mass 4kg traveling at — 5m / s j) . After the collision they stick together. What is the magnitude and direction of the velocity after the collision? 8-10 If in Problem 8-7 (iv) the collision was totally inelastic, what would be the velocity after the collision? 8—11 The Earth has a mass which is 81 times the mass of the moon. The Earth~moon distance is 4x105km. Locate the center of mass of the Earth-moon system. 8-12 The puck M1 = 2kg has a velocity of 3m/sfi when it collides with a puck, M2 = 5kg which has a velocity of ~ 6m / s 3"). , What are their velocities after the collision? 8-13 A 2kg block is lying on a smooth horizontal table. A bullet of mass 0.01kg travelling of IOOm/s 92 is fired into it and gets embedded. If the table is 2m high, where will the combination land on the ground? bill 8—14 A person of mass 50kg is standing at the end of a plank of mass 100kg and length 5m, and the plank rests on a horizontal smooth, icy surface. If the person walks from one end to the other, by how much will the plank move? Why? 8—15 (Ballistic Pendulum) Now the mass is hanging from a 1m long string when the bullet is fired. How high will the combination rise before falling back? ' ...
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