Conservation of Momentum Unit 6: Momentum, Impulse, and Conservation of Momentum

I. Momentum “mass in motion” Depends on mass and velocity of an object. Equation (See Ref. Tables): p = mv Units: kg*m/s Vector quantity: (same direction as object’s velocity)

I. Momentum Example: What is the momentum of a 40,000 kg train going 2 m/s? What is the momentum of a 2,000 kg car going 40 m/s? How do they compare? 3

II. Impulse What causes a change in velocity (acceleration)? FORCES!!! Definition: How long (time) a force acts on an object Equation (see ref. tabs) J = Fnet t = Δp Units: N*s OR kg*m/s 4

III. Relating Impulse and Momentum Example: A ball is stopped by a 100 N force over a time period of 2 s. Determine the impulse acting on the ball. 5

III. Relating Impulse and Momentum Impulse-Momentum Theorem: The impulse acting on an object is equal to the object’s change in momentum Video (1 min)- Stopping an egg against a brick wall and stopping an egg against a bed sheet Video (2 min)- Football helmets and pads decrease the force by extending the time of the impact 6

IV. Momentum and Impulse Egg Demo Questions How does the impulse of an egg being thrown against a wall compare to the impulse of an egg being thrown against a bed sheet? In terms of force and time, why does an egg thrown against a bed sheet not break, but thrown against a wall it does? The same The sheet spreads the force over a longer time, so the force is less since the impulse is the same 7

Science of Airbags – Video (3 min) V. Application of Impulse-Momentum Theorem An airbag spreads the force over a greater time, therefore decreasing the magnitude of the force acting on the person Science of Airbags – Video (3 min) 8

VI. Momentum and Impulse Examples A force of 20 N acts on a 3.5 kg mass for 10 s. What is the impulse of the object? 2. A 2,000 kg car traveling at 10 m/s accelerates to a speed of 25 m/s. What is the impulse of the car? 9

VI. Collisions and Conservation of Momentum Review of Newton’s Third Law of Motion: “For every action…” … there is an equal and opposite reaction. F on bug = - F on bus

VI. Conservation of Momentum The total momentum before the collision is equal to the total momentum after the collision. Conservation of Momentum in Space video (2 min) Equation: (see reference tables) 11

VII. Elastic Collision Elastic Collision: Objects collide and move off with different momentums (momenta) Equation: mAvAi +mBvBi = mAvAf+ mBvBf 12

mAvAi +mBvBi = mAvAf+ mBvBf VII. Elastic Collision mAvAi +mBvBi = mAvAf+ mBvBf Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s. A) What is the total momentum before the collision? 13

mAvAi +mBvBi = mAvAf+ mBvBf VII. Elastic Collision mAvAi +mBvBi = mAvAf+ mBvBf Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s. B) What is the total momentum after the collision? 14

mAvAi +mBvBi = mAvAf+ mBvBf VII. Elastic Collision mAvAi +mBvBi = mAvAf+ mBvBf Example: A 3000 kg truck traveling 10 m/s collides with a 1000 kg car at rest. After the collision, the car travels with a speed of 15 m/s. C) What is speed of the truck after the collision? 15

VIII. Inelastic Collision Objects collide and move off with the same velocity (“stick together”) Equation: mAvAi +mBvBi = (mA+ mB)vf 16

VIII. Inelastic Collision mAvAi +mBvBi = (mA+ mB)vf Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together. A) What it the total momentum before the collision? 17

VIII. Inelastic Collision mAvAi +mBvBi = (mA+ mB)vf Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together. B) What it the total momentum after the collision? 18

VIII. Inelastic Collision mAvAi +mBvBi = (mA+ mB)vf Example: An 80 kg grandma traveling 6 m/s on roller skates collides with her 40 kg grandchild initially at rest. After they collide, she picks him up and travel together. C) What is the speed of the grandma and child after the collision? 19

IX. Explosions and Recoil The total momentum before and after is equal to zero Equation: - mAvAf = mBvBf 20

IX. Explosions and Recoil -mAvAf = mBvBf Example: A 0.010 kg tennis ball is placed in a 20 kg cannon. The tennis ball is launched out of the cannon with a speed of 100 m/s. What is the total momentum before the explosion? What is the total momentum after the explosion? C) What is the recoil speed of the cannon? 21