Collisions 8.01 Week 07D2Next Reading Assignment: W07D3 Quiz 5: Energy 2Concept Question: Choice of system Drop a stone from the top of a high cliff. Consider the earth and the stone as a system. As the stone falls, the momentum of the system 1. increases in the downward direction. 2. decreases in the downward direction. 3. stays the same. 4. not enough information to decide.Concept Question: Jumping on Earth Consider yourself and the Earth as one system. Now jump up. Does the momentum of the system 1. Increase in the downward direction as you rise? 2. Increase in the downward direction as you fall? 3. Stay the same? 4. Dissipate because of friction?Strategy: Momentum of a System 1. Choose system 2. Identify initial and final states 3. Identify any external forces in order to determine whether any component of the momentum of the system is constant or not 5Table Problem: Exploding Projectile 6 An instrument-carrying projectile of mass m1 accidentally explodes at the top of its trajectory. The horizontal distance between launch point and the explosion is x0. The projectile breaks into two pieces which fly apart horizontally. The larger piece, m3, has three times the mass of the smaller piece, m2. To the surprise of the scientist in charge, the smaller piece returns to earth at the launching station. Neglect air resistance and effects due to the earth’s curvature. How far away, xf, from the original launching point does the larger piece land?Table Problem: Landing Plane and Sandbag 7 A light plane of mass 1000 kg makes an emergency landing on a short runway. With its engine off, it lands on the runway at a speed of 40 ms-1. A hook on the plane snags a cable attached to a sandbag of mass 120 kg and drags the sandbag along. If the coefficient of friction between the sandbag and the runway is µ = 0.4, and if the plane’s brakes give an additional retarding force of magnitude 1400 N, how far does the plane go before it comes to a stop?Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion? 1. Yes, it moves to the right. 2. Yes, it moves to the left. 4. No, it remains in place. Concept Question: RecoilA person of mass m1 is standing on a cart of mass m2 that is on ice. Assume that the contact between the cart’s wheels and the ice is frictionless. The person throws a ball of mass m3 in the horizontal direction (as determined by the person in the cart). The ball is thrown with a speed u with respect to the cart. a) What is the final velocity of the ball as seen by an observer fixed to the ground? b) What is the final velocity of the cart as seen by an observer fixed to the ground? Worked Example: RecoilConcept Question: Inelastic collision Cart A is at rest. An identical cart B, moving to the right, collides with cart A. They stick together. After the collision, which of the following is true? 1. Carts A and B are both at rest. 3. Carts A and B move to the right with a speed greater than cart B's original speed. 5. Carts A and B move to the right with a speed less than cart B's original speed. 6. Cart B stops and cart A moves to the right with speed equal to the original speed of cart B.Concept Question: Elastic collision Cart A is at rest. An identical cart B, moving to the right, collides elastically with cart A. After the collision, which of the following is true? 1. Carts A and B are both at rest. 3. Cart B stops and cart A moves to the right with speed equal to the original speed of cart B. 5. Cart A remains at rest and cart B bounces back with speed equal to its original speed. 4. Cart A moves to the right with a speed slightly less than the original speed of cart B and cart B moves to the right with a very small speed.Demo: Ball Bearing and Glass B60 http://tsgphysics.mit.edu/front/index.php?page=demo.php?letnum=B%2060&show=0 Drop a variety of balls and let students guess order of elasticity.Demo and Worked Example: Two Ball Bounce Two superballs are dropped from a height h above the ground. The ball on top has a mass M1. The ball on the bottom has a mass M2. Assume that the lower ball collides elastically with the ground. Then as the lower ball starts to move upward, it collides elastically with the upper ball that is still moving downwards. How high will the upper ball rebound in the air? Assume that M2 >> M1. M2>>M1Table Problem: Three Ball Bounce Three balls having the masses shown are dropped from a height h above the ground. Assume all the subsequent collisions are elastic. What is the final height attained by the lightest ball?Table Problem and Mini-Experiment: Astro-BlasterTable Problem: Slingshot A spacecraft of mass m1 = 2150 kg with a speed v1i = 10.4 km/s approaches Saturn which is moving in the opposite direction with a speed vs = 9.6 km/s . After interacting gravitationally with Saturn, the spacecraft swings around Saturn and heads off in the opposite direction it approached . The mass of Saturn is ms = 5.69 x 1026 kg. Find the final speed of the spacecraft after it is far enough away from Saturn to be nearly free of Saturn’s gravitational pull.Source Material: 1. High speed video of
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