Momentum How do we measure the momentum of an object? How is momentum conserved in collisions? Describe an example of angular momentum?

momentum = mass  velocity Chapter 6 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 As mass increase momentum increases As velocity increase momentum increases.

Day 1: Practice Problem When comparing the momentum of two moving objects, which of the following is correct? a)The object with the higher velocity will have less momentum if the masses are equal. b)The more massive object will have less momentum if its velocity is greater. c)The less massive object will have less momentum if the velocities are the same. d)The more massive object will have less momentum if the velocities are the same. What is the momentum of a 60 kg child running at 3 m/s? Answer is C

Day 2: Practice Answers : 1. C 2. p = mv = (60.0 kg) (3.0 m/s)

Day 2: Momentum is Conserved, Chapter 6 Day 2: Momentum is Conserved, Newton’s third law leads to conservation of momentum During the collision, the force exerted on each bumper car causes a change in momentum for each car. The total momentum is the same before and after the collision.

Day 2: Momentum is Conserved Chapter 6 Day 2: Momentum is Conserved The Law of Conservation of Momentum: The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. m1v1,i + m2v2,i = m1v1,f + m2v2,f total initial momentum = total final momentum

Day 2: Conservation of Momentum BOING! SPLAT! Holy Vectors Batman, its Momentum. The conservation of momentum is very important in the study of collisions (atoms, highway accidents, sports science etc..) Go to this website and observe how the different masses react in a collision. Don’t worry about the math just yet. Just predict which mass will slow down and which will speed up. http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Spcl.html#1 http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Exmpl.html#5 More advance classes may be able to do the math. The two URL’s are for the same website. The first one is for elastic collisions. The second is for inelastic collision.

Sample Problem Chapter 6 Conservation of Momentum 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?

Sample Problem, continued Chapter 6 Sample Problem, continued Conservation of Momentum 1. Define Given: m1 = 76 kg m2 = 45 kg v1,i = 0 v2,i = 0 v1,f = 2.5 m/s to the right Unknown: v2,f = ?

Sample Problem, continued Chapter 6 Sample Problem, continued Conservation of Momentum 2. Plan Choose an equation or situation: Because the total momentum of an isolated system remains constant, the total initial momentum of the boater and the boat will be equal to the total final momentum of the boater and the boat. m1v1,i + m2v2,i = m1v1,f + m2v2,f

Sample Problem, continued Chapter 6 Sample Problem, continued Conservation of Momentum 2. Plan, continued Because the boater and the boat are initially at rest, the total initial momentum of the system is equal to zero. Therefore, the final momentum of the system must also be equal to zero. m1v1,f + m2v2,f = 0 Rearrange the equation to solve for the final velocity of the boat.

Sample Problem, continued Section 2 Conservation of Momentum Chapter 6 Sample Problem, continued Conservation of Momentum 3. Calculate Substitute the values into the equation and solve:

Sample Problem, continued Chapter 6 Sample Problem, continued Conservation of Momentum 4. Evaluate The negative sign for v2,f indicates that the boat is moving to the left, in the direction opposite the motion of the boater. Therefore, v2,f = 4.2 m/s to the left

Day 3: Practice Problems 1) A roller coaster climbs up a hill at 4 m/s and then zips down the hill at 30 m/s. The momentum of the roller coaster A) is greater up the hill than down the hill. B) is greater down the hill than up the hill. C) remains the same throughout the ride. D) is zero throughout the ride. 2) In a two-body collision, A) momentum is always conserved. B) kinetic energy is always conserved. C) neither momentum nor kinetic energy is conserved. D) both momentum and kinetic energy are always conserved.

Day 3 : Practice continued 1. The law of conservation of momentum states that A) the total initial momentum of all objects interacting with one another usually equals the total final momentum. B) the total initial momentum of all objects interacting with one another does not equal the total final momentum. C) the total momentum of all objects interacting with one another is zero. D) the total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. 2. Which of the following statements about the conservation of momentum is not correct? A) Momentum is conserved for a system of objects pushing away from each other. B) Momentum is not conserved for a system of objects in a head-on collision. C) Momentum is conserved when two or more interacting objects push away from each other. D) The total momentum of a system of interacting objects remains constant regardless of forces between the objects.

Day 4: Quiz (Let’s Go!!!)