Momentum is a property of moving matter. Momentum describes the tendency of objects to keep going in the same direction with the same speed.

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1 Warm-up A mosquito collides head-on with a car traveling 60 mph. How do you think the size of the force that car exerts on the mosquito compares to the size of the force that mosquito exerts on car?

2 12.1 Momentum Momentum is a property of moving matter. Momentum describes the tendency of objects to keep going in the same direction with the same speed. Changes in momentum result from forces or create forces.

3 12.1 Momentum The momentum of a ball depends on its mass and velocity. Ball B has more momentum than ball A.

4 12.1 Momentum and Inertia Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass. Inertia is a scalar quantity. Momentum is a property of moving mass that resists changes in a moving object s velocity. Momentum is a vector quantity.

5 12.1 Momentum Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec. A 1 N force is applied to deflect the motion of each ball. What happens? Does the force deflect both balls equally? Ball B deflects much less than ball A when the same force is applied because ball B had a greater initial momentum.

6 12.1 Calculating Momentum The momentum of a moving object is its mass multiplied by its velocity. That means momentum increases with both mass and velocity. Momentum (kg m/sec) Mass (kg) p = m v Velocity (m/sec)

7 Comparing momentum A car is traveling at a velocity of 13.5 m/sec (30 mph) north on a straight road. The mass of the car is 1,300 kg. A motorcycle passes the car at a speed of 30 m/sec (67 mph). The motorcycle (with rider) has a mass of 350 kg. Calculate and compare the momentum of the car and motorcycle. 1. You are asked for momentum. 2. You are given masses and velocities. 3. Use: p = m v 4. Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s 5. Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s The car has more momentum even though it is going much slower.

8 Warm up: Cars A, B, C, and D, have twice the mass of the cars E, F, G, and H. Rank the cards in order from smallest to biggest momentum. A B C E F G D H

9 12.2 Force is the Rate of Change of Momentum changes when a net force is applied. The inverse is also true: If momentum changes, forces are created. If momentum changes quickly, large forces are involved. Momentum

10 12.2 Force and Momentum Change The relationship between force and motion follows directly from Newton's second law. Force (N) Change in time (sec) F = D p D t Change in momentum (kg m/sec)

11 Calculating force Starting at rest, an 1,800 kg rocket takes off, ejecting 100 kg of fuel per second out of its nozzle at a speed of 2,500 m/sec. Calculate the force on the rocket from the change in momentum of the fuel. 1. You are asked for force exerted on rocket. 2. You are given rate of fuel ejection and speed of rocket 3. Use F = Δp Δt = Δ(mv) Δt = (Δm Δt) v = 4. Solve: F= (100 kg/s) (-2,500 m/s) = - 250,000 kg m/s 2 The fuel exerts and equal and opposite force on rocket of +250,000 N.

12 12.2 Impulse The product of a force and the time the force acts is called the impulse. Impulse is a way to measure a change in momentum because it is not always possible to calculate force and time individually since collisions happen so fast.

13 12.2 Force and Momentum Change To find the impulse, you rearrange the momentum form of the second law. Impulse (N sec) F D t = D p Change in momentum (kg m/sec) Impulse can be expressed in kg m/sec (momentum units) or in N sec.

14 Warm up You want to close an open door by throwing either a 400-g lump of clay or a 400-g rubber ball toward it. You can throw either object with the same speed, but they are different in that the rubber ball bounces off the door while the clay just sticks to the door. Which projectile will apply the larger impulse to the door and be more likely to close it?

15 12.1 Conservation of Momentum The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change. If you throw a rock forward from a skateboard, you will move backward in response.

16 12.1 Conservation of Momentum

17 12.1 Collisions in One Dimension A collision occurs when two or more objects hit each other. During a collision, momentum is transferred from one object to another. Collisions can be elastic or inelastic.

18 12.1 Collisions

19 Elastic collisions Two kg billiard balls roll toward each other and collide head-on. Initially, the 10-ball has a velocity of 0.5 m/s. The 5- ball has an initial velocity of -0.7 m/s. The collision is elastic and the 5-ball rebounds with a velocity of 0.4 m/s, reversing its direction. What is the velocity of the 10-ball after the collision? Did it rebounded?

20 Inelastic collisions A train car moving to the right at 10 m/s collides with a parked train car. They stick together and roll along the track. If the moving car has a mass of 8,000 kg and the parked car has a mass of 2,000 kg, what is their combined velocity after the collision?