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.

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.

July 2, 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

Homework Be ready with your procedure for next class.

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 period 5 start here  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 – Ramp

Inquiry for Total Momentum Before and After a Collision/Explosion Your group will present using the whiteboards your design and findings. What did you discover about the momentum before and after a collision or explosion? What happened to the momentum before and after when one of the carts had more mass? Were any of the results NOT what you expected? Did the data support your original prediction?

Evaluation Individually, you will write an analysis about the investigation with supporting evidence, and then explain how the conservation of momentum can be applied to the investigation. Describe the investigation and the theoretical concepts related to the investigation. Can you test the predictions? What conclusion(s) did you reach due to the results of this experiment? If so, do results agree with your conclusion(s)? What evidence (text and/or data) supports your conclusion(s)? Are your results reliable? What were the sources of error and how did you compensate for sources of error in the experiment? This will be due 3 days after the conclusion of the investigations.

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