© 2010 Pearson Education, Inc. Lecture Outline Chapter 6 College Physics, 7 th Edition Wilson / Buffa / Lou

Chapter 6 Linear Momentum and Collisions © 2010 Pearson Education, Inc. Linear Momentum Impulse Conservation of Linear Momentum Elastic and Inelastic Collisions Center of Mass Jet Propulsion and Rockets

Momentum Brainstorm at least 9 things about Momentum –These can include examples. –A definition –Real World Applications –Etc.

6.1 Linear Momentum Newton referred to Momentum as “the quantity of motion arising from velocity and the quantity of matter conjointly.” Newton’s Second Law was really with momentum instead of acceleration! HOLY CRAP!

6.1 Linear Momentum Definition of linear momentum: The linear momentum of an object is the product of its mass and velocity. [For a single particle] Note that momentum is a vector. SI unit of momentum: kg m/s. This unit has no special name. © 2010 Pearson Education, Inc.

6.1 Linear Momentum For a system of objects, the total linear momentum is the vector sum of each. Find the momentum for each particle or object and then add them all up! © 2010 Pearson Education, Inc.

A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system? a) momentum of the system is positive b) momentum of the system is negative c) momentum of the system is zero d) you cannot say anything about the momentum of the system Question 6.2a Momentum and KE I

Two objects are known to have the same momentum. Do these two objects necessarily have the same kinetic energy? a) yes b) no Question 6.2c Momentum and KE III

6.1 Linear Momentum A 100 kg football player runs with a velocity of 4 m/s straight down the field. A 1.0 kg artillery shell leaves the barrel of a gun with a muzzle velocity of 500 m/s. Which has the greater momentum, the football player or the shell?

6.1 Linear Momentum Conceptual Question: Consider the following: a.22 caliber bullet, a cruise ship, and a glacier. Assuming each to be moving at its normal speed, which would you expect to have the greatest linear momentum?

6.1 Linear Momentum The change in momentum is the difference between the momentum vectors. The vector sum and the vector difference are different! © 2010 Pearson Education, Inc.

6.1 Linear Momentum

In the object changes velocity, then that means it must be _____________. If something is accelerating, that means this must be acting on it ______________. Similarly, momentum is directly related to velocity. Therefore, a change in momentum also requires a net force.

6.1 Linear Momentum If an object’s momentum changes, a force must have acted on it. The net force is equal to the rate of change of the momentum. © 2010 Pearson Education, Inc.

A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? a) greater than b) less than c) equal to Question 6.3a Momentum and Force

6.2 Impulse Impulse is the change in momentum: © 2010 Pearson Education, Inc. When two objects collide they can exert a large force on one another for a short period of time. This is called Impulse! S.I. Unit of Impulse is N s

6.2 Impulse An impulse exerted on an object is equal to the change in the objects momentum. This is called the Impulse – Momentum Theorem –Similar to Work – Energy Theorem

A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? a) the beanbag b) the rubber ball c) both the same Question 6.7 Impulse

6.2 Impulse A golfer drives a kg ball from an elevated tee, giving the ball an initial horizontal speed of 40 m/s (about 90 mi/hr). What is the magnitude of the average force exerted by the club on the ball during this time?

6.2 Impulse © 2010 Pearson Education, Inc. In some cases, contact time may be shortened to maximize the impulse. However, the contact time can also be manipulated to reduce the amount of force.

6.2 Impulse A 70 kg worker jumps stiff-legged from a height of 1.00 m onto a concrete floor. –A.) What is the magnitude of the impulse he feels on landing, assuming a sudden stop in 8.00 ms? –B.) What is the average force?

6.2 Impulse Collisions? How do you define a collision? Does there have to be some type of contact force for a collision? Collisions range from subatomic particles to automobiles in traffic accidents.

6.2 Impulse Kinetic Energy and Momentum are very closely related (they are different quantities…but still they like each other!) K = p 2 2m

6.3 Conservation of Linear Momentum If there is no net force acting on a system, its total momentum cannot change. Forces must be balanced, which means F NET is equal to ???? This is the law of conservation of momentum. © 2010 Pearson Education, Inc.

6.3 Conservation of Linear Momentum In this example, there is no external force, but the individual components of the system do change their momenta: © 2010 Pearson Education, Inc.

6.3 Conservation of Linear Momentum Collisions happen quickly enough that any external forces can be ignored during the collision. Therefore, momentum is conserved during a collision. © 2010 Pearson Education, Inc.

6.4 Elastic and Inelastic Collisions In an elastic collision, the total kinetic energy is conserved. Total kinetic energy is not conserved in an inelastic collision. © 2010 Pearson Education, Inc.

6.4 Elastic and Inelastic Collisions A completely inelastic collision is one where the objects stick together afterwards. © 2010 Pearson Education, Inc.

6.4 Elastic and Inelastic Collisions The fraction of the total kinetic energy that is left after a completely inelastic collision can be shown to be: © 2010 Pearson Education, Inc.

6.4 Elastic and Inelastic Collisions For an elastic collision, both the kinetic energy and the momentum are conserved: © 2010 Pearson Education, Inc.

6.4 Elastic and Inelastic Collisions Collisions may take place with the two objects approaching each other, or with one overtaking the other. © 2010 Pearson Education, Inc.

6.5 Center of Mass Definition of the center of mass: The center of mass is the point at which all of the mass of an object or system may be considered to be concentrated, for the purposes of linear or translational motion only. We can then use Newton’s second law for the motion of the center of mass: © 2010 Pearson Education, Inc.

6.5 Center of Mass The momentum of the center of mass does not change if there are no external forces on the system. The location of the center of mass can be found: This calculation is straightforward for a system of point particles, but for an extended object calculus is necessary. © 2010 Pearson Education, Inc.

6.5 Center of Mass The center of mass of a flat object can be found by suspension. © 2010 Pearson Education, Inc.

6.5 Center of Mass The center of mass may be located outside a solid object. © 2010 Pearson Education, Inc.

6.6 Jet Propulsion and Rockets If you blow up a balloon and then let it go, it zigzags away from you as the air shoots out. This is an example of jet propulsion. The escaping air exerts a force on the balloon that pushes the balloon in the opposite direction. Jet propulsion is another example of conservation of momentum. © 2010 Pearson Education, Inc.

6.6 Jet Propulsion and Rockets This same phenomenon explains the recoil of a gun: © 2010 Pearson Education, Inc.

6.6 Jet Propulsion and Rockets The thrust of a rocket works the same way. © 2010 Pearson Education, Inc.

6.6 Jet Propulsion and Rockets Jet propulsion can be used to slow a rocket down as well as to speed it up; this involves the use of thrust reversers. This is done by commercial jetliners. © 2010 Pearson Education, Inc.

Summary of Chapter 6 Momentum of a point particle is defined as its mass multiplied by its velocity. The momentum of a system of particles is the vector sum of the momenta of its components. Newton’s second law: © 2010 Pearson Education, Inc.

Summary of Chapter 6 Impulse–momentum theorem: In the absence of external forces, momentum is conserved. Momentum is conserved during a collision. Kinetic energy is also conserved in an elastic collision. © 2010 Pearson Education, Inc.

Summary of Chapter 6 The center of mass of an object is the point where all the mass may be considered to be concentrated. Coordinates of the center of mass: © 2010 Pearson Education, Inc.