Momentum and Collisions Momentum and Impulse

Section Objectives Compare the momentum of different moving objects. Compare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an object Describe changes in momentum in terms of force and time.

Linear Momentum Momentum is defined as a product of the mass and the velocity of an object. Momentum is mass times velocity. –Momentum is represented by the symbol, p –p = mv Momentum has the SI units of kgm/s Momentum is a vector quantity. Clip 324

Practice Problems A A 2250 kg pickup truck has the velocity of 25 m/s to the east. What is the momentum of the truck? A 21 kg child on a 5.9 kg bike is riding with a velocity of 4.5 m/s to the northwest. a)What is the total momentum of the child and the bike together? b)What is the momentum of the child? c)What is the momentum of the bike?

Force and Impulse A change in momentum takes force and time. –Ball example –Bowling Ball From these examples we see that change in momentum is closely related to force.

Impulse-momentum Theorem Force X time interval = Change in momentum F  t =  p = mv f - mv i F  t is called the impulse Force is reduced when the time interval of an impact is increased. clip 598

Sample Problems B A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in.30 s. find the force exerted on the car during the collision. A kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver catches the ball and brings it to rest in.020 s. What is the force exerted on the ball by the receiver?

Stopping Times and Distances Stopping times and distances depend on the impulse-momentum. A truck with twice the mass will take twice the distance and time to stop.

Practice Problem C A 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is 8410 N to the east? How far does the car travel during the deceleration? How long would the car in the above sample problem take to come to a stop from its initial velocity of 20.0 m/s to the west? How far would the car move before stopping? Assume a constant acceleration.

Homework P 199 1, 3 P 201 2, 3, 4 P 203 2, 3 P 204 1, 2, 3 P , 5 -7,

Conservation of Momentum

Section Objectives Describe the interaction between two objects in terms of the change in momentum of each object. Compare the total momentum of the two objects before and after they interact. State the law of conservation of momentum Predict the final velocities of objects after collisions, given the initial velocities.

Momentum is conserved This figure shows a stationary billiard ball set into motion by a collision with a moving billiard ball. Before the collision, the momentum of the green ball is zero. During the collision the blue ball losses momentum while the green ball gains. The momentum the blue ball losses is equal to the momentum gained to the green ball.

Conservation con’t In other words: Total initial momentum = total final momentum (m 1 v 1 ) I + (m 2 v 2 ) I = (m 1 v 1 ) f + (m 2 v 2 ) f For an isolated system, law of consevation of momentum can be stated as follow: –The total momentum of all objects interacting with one another remains constant regardless of the nature if the forces between the objects.

Practice Problem D A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? A 63.0 kg astronaut is on a spacewalk when the tether line to the shuttle breaks. The astronaut is able to throw a spare 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 12.0 m/s, propelling the astronaut back to the shuttle, find the astronaut’s final speed with respect to the shuttle after the tank is thrown.

Homework P 209 2, 3, 4 P P

Elastic and Inelastic Collisions

Section Objectives Identify different types of collisions Determine the changes in kinetic energy during perfectly inelastic collisions. Compare conservation of momentum and conservation of kinetic energy in perfectly inelastic and elastic collisions. Find the final velocity of an object in perfectly inelastic and elastic collisions.

Inelastic Collisions When two objects, such as the two football players, collide and move together as one mass, the collision is called a perfectly inelastic collision. See 327

Inelastic Collisions con’t Inelastic collisions are easy to analyze in terms of momentum because the objects become essentially one object after the collision. (m 1 v 1 ) i + (m 2 v 2 ) i = (m 1 +m 2 )v f

Sample Problems E A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with the mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at the velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision? A grocery shopper tosses a 9.0 kg bag of rice into a stationary 18.0 kg grocery cart. The bag hits the cart with a horizontal speed of 5.5 m/s towards the front of the cart. What is the final speed of the cart and the bag?

Kinetic energy and Collisions In an inelastic collision, kinetic energy is not conserved. The amount of kinetic energy lost can be calculated by finding the change of kinetic energy.

Sample Problems F Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.50 kg and an initial velocity of 4.0 m/s to the right. The second ball has a mass of 0.25 kg and an initial velocity of 3.0 m/s to the left. What is the decrease in kinetic energy during the collision? During practice, a student kicks a 0.40 kg soccer ball with a velocity of 8.5 m/s to the south into a 0.15 kg bucket lying on its side. The bucket travels with the ball after the collision. –What is the final velocity of the combined mass? –What is the decrease in kinetic energy during the collision?

Elastic Collisions An elastic collision occurs when two objects collide and return to their original shapes with no loss of total kinetic energy. Kinetic energy and momentum is conserved in elastic collisions. –m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f –1/2m 1 v 1,i 2 + 1/2m 2 v 2,i 2 = 1/2m 1 v 1,f 2 + 1/2m 2 v 2,f 2 Clip 600

Sample Problem G A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume hat neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface, What is the velocity of the kg marble after the collision?

Homework P 214 1, 3, 4, 5 P 216 1, 3 P P P