MOMENTUM What is momentum? What do you think about when you hear that word? What examples can you give of large or small momentum (plural is momenta).

MOMENTUM: Inertia in motion Mass X Velocity More mass, more momentum More velocity, more momentum No mass, NO momentum No velocity, NO momentum

MOMENTUM Momentum is mass X velocity p = mv The unit is kg m/s

The Law of Conservation of Momentum Momentum in a closed system is ALWAYS CONSERVED Momentum “before” an event is equal to momentum “after” an event Classic examples are explosions, car crashes, freight trains, pool balls, & shooting a gun.

Momentum conserved In a collision, if one pool ball collides into another one that is at rest, pool ball 1 “shares” some momentum with pool ball 2 The TOTAL momentum of both pool balls (or cars in a crash, etc.) added together is THE SAME before and after the collision p = p’ or mBvB = mAvA or m1v1 + m2v2 = mTvT

The Impulse Momentum Theorem CHANGE in momentum is EQUAL to Impulse IMPULSE is equal to IMPACT (or force) times the TIME INTERVAL of the impact Δp = FΔt or Δ (mv) = F Δt

Applications Why is it better to bend your knees when you jump off a table? Why do you move your hand backward when catching a fast pitch? Why do air bags help?

Change in (mv) = Impulse = Ft Why does a karate expert often try to have a SHORT time of impact?

More applications If you only want maximum velocity, such as trying to achieve maximum range of a golf ball, you should hit the ball with a) a short time of impact b) a long time of impact c) it makes no difference

Applications continued If a building is on fire and you want to minimize the force of impact on your bones when you jump from the 2nd story window, you should a) land with straight legs b) land on your feet but bend knees c) drop and roll to maximize time of impact

PELTON WHEEL Why did the PELTON wheel work BETTER than other kinds of water wheels? When was it invented? Who invented it? How were the paddles different? What does this have to do with anything?

Pelton wheel—what’s so special?

Which arrow—A or B—imparts a greater IMPULSE to the target? A. You shoot an arrow with 25 kg m/s of momentum and it sticks into the target. What is the CHANGE in the momentum (and therefore the impulse)? B. You shoot an arrow with 25 kg m/s of momentum and it bounces back off the target with a momentum of 10 kg m/s. What is the CHANGE in the momentum (and therefore the impulse) of this arrow?

ELASTIC COLLISIONS Bouncing, springy (like elastic !) The only PERFECTLY elastic collisions in real life are INSIDE ATOMS (and these are weird quantum collisions—not hitting each other in the regular sense) A perfectly elastic collision means there is NO friction and NO energy lost as heat

INELASTIC COLLISIONS Sticky Does not bounce back Not springy or elastic More energy lost as heat due to the force of friction In real life, all collisions are partly elastic and partly inelastic

A 0. 5 kg ball of putty is at rest. Another 0 A 0.5 kg ball of putty is at rest. Another 0.5 kg ball of putty comes along at 2 m/s and hits the first in a perfectly inelastic collision. A) What is the total momentum before the collision? B) What is the total momentum after the collision? C) As they slide off together, what is their velocity? D) What is conserved among the following: momentum; kinetic energy; energy; speed

A group of astronauts floating around in outer space are in a circle A group of astronauts floating around in outer space are in a circle. They throw a ball back and forth to each other. What happens? You are on a skateboard (not moving) and throw a basketball to a friend on a skateboard (also not moving).

You are standing on a frozen pond with ice skates on You are standing on a frozen pond with ice skates on. Your friend who is twice your mass is standing in front of you. You push off of each other. What happens? Who (if either of you) moves faster? The conservation of momentum is really derived from Newton’s _______ Law.

Now you are in the middle of a big frozen pond where there is ZERO friction. No ropes, nobody to help, no helicopter, etc. How can you get off the pond?

Given all variables equal except mass of the gun, which will “kick” more when fired—a gun with a) more mass, or b) less mass? If you had a space age extremely light gun so that the gun was just as light as the bullet, what would be the result?

Before the “big bang,” the total momentum in the universe was _______. How about after? Explain! Before you shoot a gun, the total momentum of the system is __________. After you shoot the gun, the total momentum is _______________ . This works by adding up the [positive] momentum of the bullet in one direction + ? ________________________________________