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

I. Momentum “mass in motion” mass velocity Depends on _______and _________of an object. Equation (See Ref. Tables): p = mv Units: kg*m/s vector __________quantity: Same direction as 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

I. Momentum Example: A 1000 kg car accelerates from rest to 30 m/s. Find the following: A. Car’s initial momentum B. Car’s final momentum C. Car’s change in momentum 4

II. Impulse Definition: How long (time) a net force acts on an object Equation (see ref. tabs) J = Fnet t = Δp Units: N*s OR kg*m/s 5

II. Impulse Force vs. Time Graph Area = 6

II. Impulse Example: A ball is stopped by a 100 N force over a time period of 2 s. Determine the impulse acting on the ball. 7

III. Relating Impulse and Momentum According to Newton’s second law, an unbalance force acting on an object causes it to accelerate. This acceleration produces a change in the object’s velocity and consequently its momentum. Equation (see ref. tabs.) Egg thrown at a sheet vs. brick wall video How football helmets protect you video 8

III. Relating Impulse and Momentum An airbag stops a person by spreading the force over a greater time, therefore decreasing the magnitude of the force acting on the person. 9

III. Relating Impulse and Momentum A baseball batter is instructed to “follow through” with his swing. This keeps the bat in contact with the ball for a longer period of time. Therefore, producing a larger impulse and larger change in the ball’s velocity. 10

IV. Momentum and Impulse Examples A force of 20.0 N acts on a 3.50 kg mass for 10.0 s. What is the impulse of the object? What is the change in speed of the object? 11

IV. Momentum and Impulse Examples 2. A 2200 kg SUV traveling 26 m/s can be stopped in 5.5 seconds in a panic stop, or in 0.22 seconds if it hits a concrete wall. What is the average force that is exerted on the SUV in each case? Panic Stop: 12

IV. Momentum and Impulse Examples 2. A 2200 kg SUV traveling 26 m/s can be stopped in 5.5 seconds in a panic stop, or in 0.22 seconds if it hits a concrete wall. What is the average force that is exerted on the SUV in each case? Concrete Wall: 13

Whiteboard Problems: If the velocity of a ball is doubled what effect does this have on the momentum of the object? A 0.05 kg baseball is approaching the batter at 30 m/s, the batter swings and hits the ball at 20 m/s back toward the pitcher. Find the change in momentum of the baseball (THINK DIRECTION) If the ball is in contact with the bat for 0.05 s, what force was applied to the ball by the bat? Find the impulse acting on a 50 kg cart to bring to rest from 10 m/s. Find the impulse of a car hitting a wall with a force of 30,000 N East and comes to a stop in 0.5 seconds. A 5 kg box is stopped with a force of 100 N over 2 seconds. Find the initial velocity of the box. doubled 2.5 kg*m/s 50 N 500 kg*m/s 15,000 N*s 40 m/s 14

Whiteboard Problems: If the force acting on an object is doubled how does this affect the impulse? A 2000 kg meteorite crashes into Earth with a speed of 10,000 m/s. If the meteorite is brought to a rest in 3.5 s, find the force from the ground that was exerted on it to bring it to a stop. How long does it take to stop a 1500 kg car if the breaking force is 9000 N and it is originally traveling 25 m/s? What is the impulse acting on a 40 kg object if it originally traveling 10 m/s and reaches a speed of 35 m/s. A 200 N force is acted on an object that is initially moving at 20 m/s. If the object is brought to a rest in 5 s, find the mass of the object. doubled 5.71 x10 6 N 4.17 s 1000 kg*m/s 50 kg 15

V. Collisions and Conservation of Momentum Review of Newton’s Third Law of Motion: “For every action (force) there is an equal and opposite (in direction) reaction (force).” F on fly = - F on bus

V. Collisions and Conservation of Momentum Because the force between two objects colliding is the same and the time they act on each other is also the same, they both experience the same magnitude in impulse, but opposite direction. Consequently, the change in its objects’ momentum is the same, but opposite in direction. This relationship is summed up in the law of conservation of momentum.

V. Collisions and Conservation of Momentum Total momentum of the objects before a collision is equal to the total momentum of the objects after. Conservation of Momentum in Space video (2 min) Conservation of Momentum Phet Simulation Equation: (see reference tables) 18

VI. Elastic Collision Elastic Collision (phet animation): Objects collide and move off with different momentums (momenta) Equation: mAvAi +mBvBi = mAvAf+ mBvBf 19

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. Find the speed of the truck after the collision. 20

mAvAi +mBvBi = mAvAf+ mBvBf VI. Elastic Collision mAvAi +mBvBi = mAvAf+ mBvBf Whiteboard Problems: A 1,000 kg car is traveling at 15 m/s North and a 2,000 kg truck is stopped at a traffic light. If the two cars collide and the Jeep’s velocity is 6 m/s North determine the car’s velocity (include direction). A 1,500 kg car traveling at 10 m/s collides with a 90 kg garbage can at rest. The garbage can flies forward at 20 m/s, find the velocity of the car. A 5.00 kg ball traveling east collides with a 9.00 kg block moving 6.00 m/s west. The ball recoils (goes backwards (keep in mind of direction)) with a velocity of 2.00 m/s west and block keeps moving west with a velocity of 1.00 m/s. What was the ball’s velocity before the collision? 3 m/s North 8.87 m/s 7.0 m/s 21

VII. Inelastic Collision Inelastic Collision (phet animation): Objects collide and move off with the same velocity (“stick together”) Equation: mAvAi +mBvBi = (mA+ mB)vf 22

VII. 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. Find their speed after they collide. 23

VIII. Inelastic Collision mAvAi +mBvBi = (mA+ mB)vf Whiteboard Problems: Two freight cars, each with a mass of 3 X 105 kg, collide. One was initially moving at 2.2 m/s; the other was at rest. They stick together. What is their final speed? A 2575 kg sleigh runs into the back of an 825 kg car at rest. They move off together at 8.5 m/s. Assuming the friction with the road can be negligible, find the initial speed of the sleigh. A 10 kg cart traveling at 2 m/s overtakes and collides with a 5 kg cart moving in the same direction. If the two carts lock together at travel at 1.5 m/s, how fast was the 5 kg cart moving? 1.1 m/s 11.2 m/s 0.5 m/s 24

VIII. Explosions and Recoil The total momentum before and after is equal to zero Equation: - mAvAf = mBvBf 25

VIII. 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. Find the recoil speed of the cannon. 26

VIII. Explosions and Recoil -mAvAf = mBvBf Whiteboard Problems: A soda bottle (m = 0.1 kg) filled with a flammable vapor is ignited and a rubber stopper (m = 0.01 kg) is fired across the room at 100 m/s. Find the recoil velocity of the soda bottle. Gene and Lynn are skating on a pond. Gene (80 kg) pushes off of Lynn (60 kg) while standing still. Gene is moving at 2 m/s after pushing off, how fast is Lynn moving? A 0.02 kg bullet is fired from a 8 kg rifle. The rifle recoils with a velocity of 2 m/s. What is the velocity of the bullet? 1.1 m/s 2.7 m/s 800 m/s 27