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Conservation of Momentum Conservation of Momentum • Allows us to determine what happens in collisions or explosions • The total momentum of all objects before a collision must equal the total momentum after the collision *objects with the same mass will exchange velocities Explosions • Are a collision of sorts before the explosion the momentum is often zero – the object is at rest. Ex: firecrackers • After the explosion, parts of the object go off in different directions *pay attention to the directions 1. A 31 kg swimmer runs with a horizontal velocity of 4 m/s off a boat dock into a stationary 8 kg rubber raft. Find the velocity that the swimmer and raft would have after the impact, if there were no friction or resistance due to the water. 2. A 275 kg bumper car containing one rider is traveling at 3.2 m/s when it bumps a stationary car containing 2 riders (345 kg). The 275 kg car bounces back with a speed of 1.7 m/s. What is the speed and direction of the 345 kg car? 3. A 60 kg astronaut becomes separated in space from her spaceship. She is 15.0 m away from it and at rest relative to it. In an effort to get back, she throws a 700-g wrench in a direction way from the ship with a speed of 8.0 m/s. How long does it take her to get back to the ship? Ballistic Pendulum Collision with a bullet and a pendulum *find the final velocity of the bullet/pendulum with conservation of momentum *find the max. height reached with conservation of energy Ballistic Pendulum 4. A 0.05 kg bullet with a velocity of 150 m/s is shot into a 3 kg ballistic pendulum initially at rest. Determine how high the pendulum rises after the bullet is shot into it. Elastic and Inelastic Collisions Regardless of the type of collision the momentum is always conserved Inelastic Collisions - a collision in which kinetic energy is lost *KEbefore ≠ KEafter - the KE lost is converted most often to friction (thermal energy) or to the energy to produce a sound or light - often involve objects that stick together Elastic and Inelastic Collisions Elastic Collision - when no kinetic energy is lost, the collision is said to be perfectly elastic - only in elastic collisions are both momentum and kinetic energy are conserved *KEbefore = KEafter - objects usually bounce off each other * you must check KE values to determine whether you have an inelastic or elastic collision 5. A toy car (4 kg) is initially moving with a velocity of 2.0 m/s when it collides with a 6 kg toy truck initially moving at -4.0 m/s. After the collision the toy truck has a velocity of 0.8 m/s. What is the velocity of the car? Is the collision elastic or inelastic? Justify your answer 6. A 15 kg medicine ball is thrown at a velocity of 5.5 m/s to a 60 kg person who is at rest on the ice. The person catches the ball and they begin sliding across the ice. Determine the velocity of the person/ball combination after the collision. Is the collision elastic or inelastic? Justify your answer 7. Several students are riding in bumper cars at an amusement park. The combined mass of car A and its occupants is 250 kg. The combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B and moving to the right at 2.0 m/s, as shown, when the driver decides to bump into car B, which is at rest. • (a) Car A accelerates at 1.5 m/s2 to a speed of 5.0 m/s and then continues at constant velocity until it strikes car B. Calculate the total time for car A to travel the 15 m. (b) After the collision, car B moves to the right at a speed of 4.8 m/s. i. Calculate the speed of car A after the collision ii. Indicate the direction of motion of car A after the collision. _________to the left ________to the right _______None; car A is at rest (c) Is this an elastic collision? ______yes _______no Justify your answer