Chapter 7 Linear Momentum

Objectives Students should be able to: 1. Define linear momentum and calculate it. 2. Distinguish between the unit of force and momentum. 3. design an experiment in order to make conclusions about the total momentum in a system before and after a collision or explosion.

Units of Chapter 7 Momentum and Its Relation to Force Conservation of Momentum Collisions and Impulse Conservation of Energy and Momentum in Collisions Elastic Collisions in One Dimension

Inelastic Collisions Collisions in Two or Three Dimensions Center of Mass (CM) CM for the Human Body Center of Mass and Translational Motion Units of Chapter 7

Let’s start with everyday language What do you say when a sports team is on a roll? They may not have the lead but they may have ___________ MOMENTUM A team that has momentum is hard to stop.

Momentum Defined p = m v p = momentum vector m = mass v = velocity vector

Momentum Momentum depends on the mass of an object and the speed it is going. –Momentum = mass x velocity Because velocity has direction then momentum does, also.

Momentum of Objects Put the following in the order of most momentum to least: –Mosquito –Automobile –Space Shuttle –Bullet –Freight Train

Questions Does a small object always have less momentum than a large one? How can a bullet from a rifle knock over an animal?

Which has more momentum? A truck or a roller skate rolling down a hill with the same speed? A truck stopped at a light or a marble rolling down the road? When could the roller skate and the truck have the same momentum?

What is Momentum? An object with a lot of momentum is also hard to stop Momentum = ρ = mv Units: kg∙m/s m=mass v=velocity Momentum is also a vector (it has direction)

Momentum  Momentum is _________ in ________.  Momentum is a vector quantity.  Momentum is dependant on the mass and the ___________ of an object. MASS MOTION VELOCITY

Momentum Facts p = m v Momentum is a vector quantity! Velocity and momentum vectors point in the same direction. SI unit for momentum: kg · m /s (no special name). Momentum is a conserved quantity (this will be proven later). A net force is required to change a body ’ s momentum. Momentum is directly proportional to both mass and speed. Something big and slow could have the same momentum as something small and fast.

Momentum Examples 10 kg 3 m /s 10 kg 30 kg · m /s Note: The momentum vector does not have to be drawn 10 times longer than the velocity vector, since only vectors of the same quantity can be compared in this way. 5 g 9 km /s p = 45 kg · m /s at 26º N of E 26º

Equivalent Momenta Bus: m = 9000 kg; v = 16 m /s p = 1.44 ·10 5 kg · m /s Train: m = 3.6 ·10 4 kg; v = 4 m /s p = 1.44 ·10 5 kg · m /s Car: m = 1800 kg; v = 80 m /s p = 1.44 ·10 5 kg · m /s continued on next slide

Equivalent Momenta (cont.) The train, bus, and car all have different masses and speeds, but their momenta are the same in magnitude. The massive train has a slow speed; the low-mass car has a great speed; and the bus has moderate mass and speed. Note: We can only say that the magnitudes of their momenta are equal since they ’ re aren ’ t moving in the same direction. The difficulty in bringing each vehicle to rest--in terms of a combination of the force and time required--would be the same, since they each have the same momentum.

7-1 Momentum and Its Relation to Force Momentum is a vector symbolized by the symbol p, and is defined as The rate of change of momentum is equal to the net force: This can be shown using Newton’s second law. (7-1) (7-2)

November 21, 2015 Newton’s Law and Momentum Newton’s Second Law can be used to relate the momentum of an object to the resultant force acting on it The change in an object’s momentum divided by the elapsed time equals the constant net force acting on the object

Problem  A 1200 kg car drives west at 25 m/s for 3 hours. What is the car’s momentum?  Identify the variables: 1200 kg = m 25m/s, west = v 3 hours = t p = mv p = (1200kg)(25m/s) = kgm/s, west

Copyright © 2009 Pearson Education, Inc. Example 7-1: Force of a tennis serve. For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mi/h). If the ball has a mass of kg and is in contact with the racket for about 4 ms (4 x s), estimate the average force on the ball.

Copyright © 2009 Pearson Education, Inc. Example 7-1: Force of a tennis serve. For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mi/h). If the ball has a mass of kg and is in contact with the racket for about 4 ms (4 x s), estimate the average force on the ball. Would this force be large enough to lift a 60-kg person?

Copyright © 2009 Pearson Education, Inc. Example 7-2: Washing a car: momentum change and force. Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it. (That is, we ignore any splashing back.) What is the force exerted by the water on the car?

Homework Be ready with your procedure for next class. In two days, complete chapter 7 problems 1, 3, and 5.

Leading to Inquiry for Total Momentum of a System Before and After a Collision or explosion  Each group will have a different type of collision or explosion. Some will overlap since we will focus on three types of collisions/explosions.

© Shannon W. Helzer. All Rights Reserved. Momentum – Elastic Collisions  Elastic Collision – a collision in which the colliding bodies do not stick together.

© Shannon W. Helzer. All Rights Reserved. Momentum – Inelastic Collisions  Inelastic Collision – a collision in which the colliding bodies stick together.

Explosions “before” M “after” m1m1 m2m2 v1v1 v2v2

© Shannon W. Helzer. All Rights Reserved. Momentum  Identify the number and types of collisions in the animation below.

© Shannon W. Helzer. All Rights Reserved. Momentum  Identify the number and types of collisions in the animation below.

© Shannon W. Helzer. All Rights Reserved. Momentum  Identify the number and types of collisions in the animation below.

Inquiry for Total Momentum Before and After a Collision/Explosion PROBLEM Design an experiment to demonstrate the effect of a collision/explosion on total momentum of the objects before and after using the same mass for each cart and then for a second experiment change one of the cart’s mass by adding mass.

Inquiry for Total Momentum Before and After a Collision/Explosion Design an experiment to demonstrate the effect of a collision/explosion on total momentum of the objects before and after using the same mass for each cart and then for a second experiment change one of the cart’s mass by adding mass to it. Make a prediction on the effect of some condition on the total momentum before and after a collision. Materials – Dynamics cart with spring bumper or plunger – Meter stick – Stop watch – Masses – Large white boards

Inquiry for Total Momentum Before and After a Collision/Explosion Your group will present using the whiteboards your design and findings. Did anything unusual happen? Were there any special insights you gained and want to make a note of? Were there any changes made to your procedure? What new questions arose? Were any of the results NOT what you expected? Which of your pre-lab ideas have you decided are now incorrect? Why? Did the data support your original hypothesis? If not, what hypothesis does the data support?

Objectives: The student will be able to: Perform several investigations in order to make conclusions about the total momentum in a system before and after collisions or explosions.

Inquiry for Total Momentum Before and After a Collision/Explosion Design an experiment to demonstrate the effect of a collision/explosion on total momentum of the objects before and after using the same mass for each cart and then for a second experiment change one of the cart’s mass by adding mass to it. Make a prediction on the effect of some condition on the total momentum before and after a collision. Materials – Dynamics cart with spring bumper or plunger – Meter stick – Stop watch – Masses – Large white boards

Inquiry for Total Momentum Before and After a Collision/Explosion Your group will present using the whiteboards your design and findings. Did anything unusual happen? Were there any special insights you gained and want to make a note of? Were there any changes made to your procedure? What new questions arose? Were any of the results NOT what you expected? Which of your pre-lab ideas have you decided are now incorrect? Why? Did the data support your original hypothesis? If not, what hypothesis does the data support?

Evaluation Individually, you will make a claim about each investigation with supporting evidence, and then explain how the conservation of momentum can be applied to these investigations. What conclusion(s) did you reach due to the results of this experiment? What evidence supports your conclusion(s)? Are your results reliable? How did you compensate for sources of error in the experiment? Can you test the predictions? If so, do results agree with your conclusion(s)? What new problems/questions does the experiment bring up? RELATE What are some possible applications of your conclusions to the real world situations? Do the results of your experiment fit any laws/theories of physics? This will be due.

Conclusions Based on the investigations, what conclusion can you make about the momentum in a system? Kahoot 7-1