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Name Date Pd Unit IX: Worksheet 3 1. A ball of mass 3.0 kg, moving at 2 m/s eastward, strikes head-on a ball of mass 1.0 kg that is moving at 2 m/s westward. The balls stick together after the impact. What are the magnitude and direction of the velocity of the combined mass after the collision? m1v1 + m2v2 = m1fv1f + m2fv2f (3.0kg)(+2m/s) + (1.0kg)(-2m/s) = (3.0kg + 1.0kg)vf (+6kg m/s + -2kg m/s)/ (4.0kg) = vf = +1m/s 2. One way of measuring the muzzle velocity of a bullet is to fire it horizontally into a massive block of wood placed on a cart. Assuming no friction, we then measure the velocity with which the wood containing the bullet and cart begin to move. In one experiment the bullet had a mass of 50. g and the wood and its cart had a mass of 10. kg. After the shot, the cart, wood, and bullet moved at a constant speed, traveling 0.80 m in 0.40 s. From this data determine the original speed of the bullet. m1v1 + m2v2 = m1fv1f + m2fv2f (0.050kg)(v) + (10.kg)(0m/s) = (10.050kg)(.80m/.40s) v = (20.1kg m/s)/(0.050kg) v = 402 m/s 3. A raft of mass 180 kg carries two swimmers of mass 50. kg and 80. kg. The raft is initially floating at rest. The two swimmers simultaneously dive off opposite ends of the raft, each with a horizontal velocity of 3 m/s. With what velocity and in what direction does the raft start to move? m1v1 + m2v2 + m3v3 = m1fv1f + m2fv2f + m3fv3f (50. kg)(0m/s) + (180kg)(0m/s) + (80kg)(0m/s) = (50kg)(-3m/s) + (180kg)(v2) + (80kg)(+3m/s) 0 = -150kg m/s + (180kg)(v2) + (+240 kg m/s) (-90kg m/s)/(180kg) = v2 V2 = -0.50m/s 4. Discuss the following in terms of impulse and momentum: a. Why are padded dashboards safer in automobiles? (increase the time during impact) b. Why are nylon ropes, which stretch considerably under stress, favored by mountain climbers? (during acceleration to a stop, the stretch increases the time for the event, thus reducing the magnitude of the acceleration and force on climber) c. Why is it preferred that railroad cars be loosely coupled with slack between cars? (allows the cars to navigate curves and offers a linking system that does not require materials that are impossibly strong. Flexible with changes in weather) ©Modeling Workshop Project 2006 1 Unit IX ws3 v3.0 5. If you throw a ball horizontally while standing on roller skates, you roll backwards. Will you roll backwards if you go through the motions of throwing the ball, but hold on to it instead? Explain your reasoning. No, because momentum is conserved. The skater and ball have no initial momentum and if the ball still has no zero velocity, the skater must also share this characteristic.) 6. Why is it difficult for a fire-fighter to hold a hose that ejects large amounts of high-speed water? (the water has mass and velocity in one direction, so the hose must also conserve momentum by with the product its mass and velocity equal in magnitude, but opposite in direction to the water.) 7. If a Mack truck and a Geo traveling at equal speeds have a head-on collision, which vehicle will experience the greatest force of impact? FMack truck Geo = -FGeo M ack truck Which will experience the greatest change in momentum? Because the magnitude of the force and time of impact is identical for each object, the changes in momentum would also be equal. Which will experience the greatest acceleration? Acceleration is governed by Newton’s 2nd law (a = F/m), therefore the smaller mass will experience the greater magnitude of acceleration because the same force is divided by a small number. 8. A billiard ball will stop short when it collides head-on with another ball which is at rest. The ball cannot stop short, however, if the collision is not exactly head-on but is at an angle. Explain why this is so in terms of momentum. If the collision is at an angle, then the conservation of momentum is related to the portion of the objects mass acting in the exact opposite direction of the second object. The fraction of the velocity of the first object not aligned with the motion of the second ball will mandate that the first object continue moving. ©Modeling Workshop Project 2006 2 Unit IX ws3 v3.0