I. Momentum Product of an objects mass and velocity. ρ = mv Units for momentum are Momentum is a vector. The direction of momentum is the same as the direction of the velocity. A 1000-kg elephant and a 0.01-kg ant are traveling down Church Street with the same momentum. If the elephant is traveling at 2 m/s, how fast is the ant traveling. (200000 m/s)

II. Impulse The product of the net force and the time interval over which it acts Impulse = FNET Δt Units for impulse are Ns Note that the units for impulse are the same as the units for momentum. . Impulse Is equal to the area under the curve of a force-time graph.

III. Impulse-Momentum Theorem Impulse is equal to the change in momentum for an object. This is a restatement of Newton’s 2nd Law By increasing the time of a collision you can decrease the amount of force and achieve the same result.

IV. Impulse-Momentum Problem Example: A 0.144 kg baseball is pitched horizontally at +38 m/s. After it is hit by a bat, it moves horizontally at –38 m/s. What impulse did the ball receive? If the bat were in contact with the ball for 0.0008 s, what force did the bat exert on the ball? Find the acceleration of the ball during its contact with the bat.

Impulse – Momentum Practice Problems Jim strikes a 0.058-kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was the club in contact with the ball? (0.013 s) A force of 186 N acts on a 7.3-kg bowling ball for 0.40 s. What is the change in velocity for the bowling ball? (10.2 m/s) A 0.24-kg volleyball approaches Taylor with a velocity of -3.8 m/s. Taylor bumps the ball giving it a velocity of 2.4 m/s. What average force did she apply if the interaction time between her hands and the ball is 0.0254 s. (58.6 N)

Egg Drop Save the egg with impulse.

V. Systems A system is a defined collection of objects. Your system is what you are working with in a problem. A system is closed if objects neither enter or leave it. A system is isolated if there is not net external force.

VI. Internal and External Force An internal force is within your system. An external force is not in your system. When the net external force on your system is zero, the system is said to be isolated.

VII. Conservation of Momentum Momentum in a closed, isolated system does not change. Momentum within the system is transferred to different objects within the system. In the example of a kicked soccer ball, the momentum of the kickers foot is transferred to the ball.

Conservation of Momentum (cont.) Another way of stating the Law of Conservation of Momentum is to say that that momentum before a collision is equal to the momentum after a collision. The change in momentum for the system is zero. http://www.physicsclassroom.com/mmedia/momentum/momentumTOC.html http://library.thinkquest.org/27948/momentum.html

VIII. Conservation of Momentum Practice Problems A 550-kg car traveling at 24.0 m/s collides head-on with a 680-kg pick-up truck. Both vehicles come to a complete stop on impact. A. What is the change in momentum of the car? (-13200 kgm/s) B. What is the change in momentum of the truck? (13200 kgm/s) C. What was the velocity of the truck before the collision? (-19.4 m/s)

IX. Elastic and Inelastic collisions In an elastic collision, the objects that collide do not stick together. Example: Getting hit in the side of the head with a ball. In an inelastic collision, the objects that collide stick together. Example: Catching a ball. http://library.thinkquest.org/27948/collision.html

http://www.physicsclassroom.com/class/momentum/u4l1b.cfm http://www.youtube.com/watch?v=eQ3RfKPPO2o&feature=related&safety_mode=true&persist_safety_mode=1

X. Elastic and Inelastic Example Problems A 0.105-kg hockey puck moving at 48 m/s is caught by a 75-kg goalie at rest. With what speed does the goalie slide on the ice?

Two opposing hockey player , one of mass 82-kg skating north at 6 Two opposing hockey player , one of mass 82-kg skating north at 6.0 m/s and the other of mass 70 kg skating south at 3.0 m/s collide and get tangled. In what direction and with what velocity do they move after the collision? ( 1.86 m/s North)

Elastic and Inelastic Example Problem A 35.0-g bullet moving at 475 m/s strikes a 5.0-kg stationary block. If the bullet leaves the block traveling at 275 m/s, how fast is the block moving after the collision?

XI. Conservation of Momentum Momentum is also conserved if you are dealing in two dimensions. You have to look at the x-direction separate from the y-direction, just as we did in the last unit.

XII. More Practice Problems 1. A 6500-kg freight car traveling at 2.5 m/s collides with a 8000-kg stationary freight car in an inelastic collision. How fast is each car moving after the collision? (1.1 m/s, 1.1 m/s)

2. Two lab carts are pushed together with a spring mechanism compressed between them. Upon release, the 5.0-kg cart repels one way with a velocity of 0.12 m/s while the 2.0-kg cart goes in the opposite direction. What velocity does it have? (0.30 m/s)

` 3. Tim, m=42.0 kg, is riding a skateboard, m=2.0 kg, traveling at 1.2 m/s. Tim jumps off the skateboard and the skateboard stops dead in its tracks. In what direction and with what velocity did he jump? (1.26 m/s in the same direction he was riding)