Transcript File
Lesson 6.2 Conservation of Momentum Essential Question: What is the conservation of momentum? Before we start… Think of the relay event in short track speed skating. One skater completes a lap and then pushes a teammate to continue skating. What happens to the skater who is pushed? What do you think? • Two skaters have equal mass and are at rest. They are pushing away from each other as shown. • Compare the forces on the two girls. • Compare their velocities after the push. • How would your answers change if the girl on the right had a greater mass than her friend? • How would your answers change if the girl on the right was moving toward her friend before they started pushing apart? A stationary billiard ball is set into motion by a collision with a moving billiard ball. Both balls are on a smooth table and neither ball rotates before or after the collision. Momentum During Collisions • When the bumper cars collide, F1 = -F2 so F1t = -F2t, and therefore p1 = -p2 . • The change in momentum for one object is equal and opposite to the change in momentum for the other object. • Total momentum is neither gained not lost during collisions. What is the law of conservation of momentum? 𝑚1 𝑣1,𝑖 + 𝑚2 𝑣2,𝑖 = 𝑚1 𝑣1,𝑓 + 𝑚2 𝑣2,𝑓 Total initial momentum = total final momentum In general, the total momentum remains constant for a system of objects that interact with one another. Momentum is conserved in collisions. What about objects pushing away from each other? Momentum is still conserved here. Imagine two skaters pushing away from each other. The skaters are both initially at rest with a momentum of zero. When they push away from each other, they move in opposite directions with equal but opposite momentum so that the total final momentum is also zero. A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? A 63.0 kg astronaut is on a spacewalk when the tether line to the shuttle breaks. The astronaut is able to throw a spare 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 12.0 m/s, propelling the astronaut back to the shuttle. Assuming that the astronaut starts from rest with respect to the shuttle, find the astronaut’s final speed with respect to the shuttle after the tank is thrown. An 85.0 kg fisherman jumps from a dock into a 135.0 kg rowboat at rest on the west side of the dock. If the velocity of the fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity of the fisherman and the boat? Each croquet ball in a set has a mass of 0.50 kg. The green ball, traveling at 12.0 m/s, strikes the blue ball, which is at rest. Assuming that the balls slide on a frictionless surface and all collisions are head-on, find the final speed of the blue ball in each of the following situations: a. The green ball stops moving after it strikes the blue ball b. The green ball continues moving after the collision at 2.4 m/s in the same direction. A boy on a 2.0 kg skateboard initially at rest tosses an 8.0 kg jug of water in the forward direction. If the jug has a speed of 3.0 m/s relative to the ground and the boy and skateboard move in the opposite direction at 0.60 m/s, find the boy’s mass. A 44 kg student on in-line skates is playing with a 22 kg exercise ball. The student is holding the ball, and both are at rest. The student then throws the ball horizontally, causing the student to glide back at 3.5 m/s. What is the final velocity of the ball? Newton’s third law leads to conservation of momentum. The impulse on the mass of object 1 is equal to and opposite the impulse on the mass of object 2. This relationship is true in every collision or interaction between two isolated objects. In every interaction between two isolated objects, the change in momentum of the first object is equal to and opposite the change in momentum of the second object. If the momentum of one object increases after a collision, then the momentum of the other object in the situation must decrease by an equal amount. In a real collision, the forces may vary in time in a complicated way. The time-averaged force during a collision is equal to the constant force required to cause the same change in momentum as the real, changing force. A boy stands at one end of a floating raft that is stationary relative to the shore. He then walks in a straight line to the opposite end of the raft, away from the shore. a. Does the raft move? Explain. b. What is the total momentum of the boy and the raft before the boy walks across the raft? c. What is the total momentum of the boy and the raft after the boy walks across the raft? What is the conservation of momentum?