Linear Momentum

1. Linear Momentum why is more force needed to stop a train than a car if both travel at the same speed? why does a little tiny bullet have so much impact? how do you steer a satellite or shuttle in space?

2. Momentum (p) a term which describes the product of mass and velocity • changing momentum depends upon changing either mass or velocity • the train is harder to stop than the car because its larger mass means a greater change in momentum • a bullet has a tremendous impact because its change in speed upon impact is extremely large- hence a large change in momentum

3. Momentum depends directly upon mass and directly upon velocity: units: kg • m/s p = mv A change in momentum usually means a change in velocity. A change in momentum will only occur if a force acts upon the object and changes its velocity (it accelerates the object!)

4. Law of Conservation of Momentum the total (vector sum) momentum of two (or more) objects before a collision will be the same as after the collision! • a collision simply means a force acted over a relatively short period of time! an explosion would be a collision! There are two types of collisions: • Inelastic- kinetic energy is not conserved • Elastic- kinetic energy is conserved

5. A 1.20 kg cart heading east at .50 m/s collides head on with a 1.60 kg cart heading west at .70 m/s and they lock together. What is the velocity of the two carts afterward? pbefore = pafter m1 = 1.20 kg m1v1 + m2v2 = (m1 + m2)v v1 = .50 m/s (1.20 kg)(.50 m/s)+(1.60 kg)(-.70 m/s) m2 = 1.60 kg = (1.20 kg + 1.60 kg)v v2 = -.70 m/s .60 + (-1.12) = 2.80v v = ? v = -.19 m/s Is this collision elastic? or .19 m/s West

6. An 6.00 kg bowling ball traveling at 2.00 m/s collides with an 8.00 kg ball that is at rest. After the collision, the 6.00 kg ball is reduced in speed to .500 m/s. What is the speed of the other ball after? pbefore = pafter m1 = 6.00 kg v1 = 2.00 m/s m1v1 + m2v2 = m1v1 + m2v2 m2 = 8.00 kg (6.00 kg)(2.00 m/s) + 0 = v2 = 0 (6.00 kg)(.500 m/s) + (8.00 kg)(v2) v1 = .500 m/s v2 = 12.0 - 3.00 =1.13 m/s v2= ? Elastic? 8.00

7. A little red wagon with a mass of 75.0 kg is rolling along when a 210.0 kg mail sack is dropped into the wagon. The wagon and the mail sack continue to roll along at 1.37 m/s. What was the speed of the little red wagon before the mail sack was dropped on it? A bowling ball of mass 6.0 kg is traveling at 4.0 m/s when it collides with an 8.0 kg ball. After the collision, the second ball accelerates to 4.75 m/s and the first is traveling 1.0 m/s opposite of its initial direction. What was the velocity of the second ball initially?

8. Is the previous collision an elastic or inelastic collision? While on a space walk, a 75.0 kg astronaut, initially at rest relative to the shuttle, throws a hammer with a speed of 4.00 m/s. If the mass of the hammer is 3.00 kg, what is the resulting velocity of the astronaut? A second astronaut, mass 85.5 kg, initially at rest, catches the thrown hammer. What is his resultant velocity?

9. A .300 kg dynamics cart traveling at .650 m/s collides with a second, identical cart at rest. They stick together after the collision. Find their velocity after and find how much kinetic energy was lost during the collision. An 86.0 kg running back heading north at 9.00 m/s is hit head on by a 92.0 kg linebacker going south at 6.00 m/s. Assume the linebacker wraps up well and find their velocity immediately after they collide.