Momentum and Collisions. Chapter 6. Table of Contents. Section 1 Momentum and Impulse. Section 2 Conservation of Momentum

Transcription

1 Table of Contents Momentum and Section 2 Conservation of Momentum 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. Section 1 Momentum and Linear Momentum Momentum is defined as mass times velocity. Momentum is represented by the symbol p, and is a vector quantity. p = mv momentum = mass velocity Image: 1

2 Linear Momentum, continued The product of the force and the time over which the force acts on an object is called impulse. The impulse-momentum theorem states that when a net force is applied to an object over a certain time interval, the force will cause a change in the object s momentum. F t = p = mv f mv i force time interval = change in momentum Movie 1 -Momentum Theorem Movie 2 F t = p = mv f mv i Practice Problem 6A p. 209 A 21 kg child is riding a 5.9 kg bike 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? Imag e: cyclin gsiste rs.org /files/ cyclin gsiste rs/ima ges/w heelm en%2 0trick %20ri ding %20c hampi on- 2.bm p Answers: 1.2 x 10 2 kg m/s; 94 kg m/s; 27 kg m/s 2

3 Practice Problem 6B p A 0.50 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 s. What is the force exerted on the receiver? Imag e: cache.daylif e.com /imag eserv e/016 7cf8b gk0l g/340 x.jpg Answer: 380 N to the right Practice Problem 6c p A 2500 kg car traveling to the north is slowed down uniformly from an initial velocity of 20.0 m/s by a 6250 N braking force acting opposite the car s motion. Use the impulse-momentum theorem to answer the following questions. a. What is the car s velocity after 2.50 s? b. How far does the car move during 2.50 s? c. How long does it take the car to come to a complete stop? Image: car_800.jpg Answers: a. 14 m/s north; b. 42 m to the north; c. 8.0 s Practice Problem 6c p Assume that the car in Sample Problem 6C has a mass of 3250 kg. a. How much force would be required to cause the same acceleration as in item 1? Use the impulse-momentum theorem? b. How far would the car move before stopping? Image: _front3.jpg Answers: a x 10 4 N to the east; b m to the west 3

4 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. Perfectly inelastic collision A collision in which two objects stick together after colliding and move together as one mass is called a perfectly inelastic collision. Conservation of momentum for a perfectly inelastic collision: m 1 v 1,i + m 2 v 2,i = (m 1 + m 2 )v f total initial momentum = total final momentum Collision movie Practice Problem p. 224 Perfectly inelastic collisions 2. 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 toward the front of the cart. What is the final speed of the cart and bag? Answer: 1.8 m/s 4

5 Sample Problem Kinetic Energy in Perfectly Inelastic Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of kg and an initial velocity of 3.00 m/s to the left.what is the decrease in kinetic energy during the collision? Elastic Elastic Collision A collision in which the total momentum and the total kinetic energy are conserved is called an elastic collision. Momentum and Kinetic Energy Are Conserved in an Elastic Collision Sample Problem, continued Elastic A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume that 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? Is kinetic energy conserved? KE is conserved ( J) 5

6 Inelastic Types of Summary 3 types of collisions 1. Perfectly inelastic; p is conserved 2. Inelastic; p is conserved 3. Elastic; both p and KE are conserved Collision summary 6