Momentum and Collisions

Momentum and Collisions

Objectives: You Should Be Able To: Define and give examples of impulse and momentum along with appropriate units. Write and apply a relationship between impulse and momentum in one dimension. State the law of conservation of momentum and apply it to the solution of problems.

What is Momentum? Momentum (p) is product of mass and velocity p = mv Units: kg m/s Momentum is a vector quantity that points in the same direction as the velocity vector: Slide 9-3

Momentum and the Impulse-Momentum Theorem 2015 Pearson Education, Inc. Slide 9-4

What causes a change in momentum ( p)? Dropping a ball During drop? Collision with surface?

Impulse (J) is a force F acting for an interval t. The impulse is a vector quantity, pointing in the direction of the average force vector IMPULSE (J) J = F ave t Units: N s Normally, a force acting for a short interval is not constant.

Finding the impulse on a bouncing ball A rubber ball experiences the force shown in FIGURE 9.4 as it bounces off the floor. a. What is the impulse on the ball? b. What is the average force on the ball? 2015 Pearson Education, Inc. Slide 9-7

Proof of Link between Impulse and Momentum Impulse F v i m t v f F m v f v A block moving with an initial velocity v i is acted on by a constant force F for a time t. i a t F t v f v mv f mv i i F m t FΔt Impulse Impulse Momentum theorem When an impulse is applied to an object it changes it s momentum

QuickCheck 9.6 Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed? A. Ball 1 B. Ball 2 C. Both balls have the same final speed. 2015 Pearson Education, Inc. Slide 9-10

A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is that of the heavy steel cart. A. Greater than B. Equal to C. Less than D. Can t say. It depends on how big the force is. Same force, same time same impulse Same impulse same change of momentum 2015 Pearson Education, Inc. Slide 9-11

Momentum and Impulse Momentum and Impulse F ave t p The rate in change of momentum is equal to the net force applied to it F( ave ) p t i.e. the more momentum an object has the harder it is to stop Or the longer to change to momentum the lower the force! When you jump off of some high thing, why is it better to bend your legs? https://www.youtube.com/watch?v=yy6imlouaso

You drop an egg onto 1) the floor 2) a thick piece of foam rubber. In both cases, the egg does not bounce. In which case is the impulse greater? A) Floor B) Foam I = P C) the same In which case is the average force greater Same change in momentum A) Floor B) Foam C) the same p = F t F = p/ t Smaller t = large F

A 50-g golf ball leaves the face of the club at 20 m/s. If the club is in contact for 0.002 s, what average force acted on the ball? F mv t

Bouncy vs. Sticky Which ball has greater change in momentum? In which case is the impulse higher?

A 500-g baseball moves to the left at 20 m/s striking a bat. The ball leaves in the opposite direction at 40 m/s. What was impulse on ball? + m = 0.5 kg 20 m/s - + t F 40 m/s What is the impulse if the ball stuck to the bat?

QuickCheck 9.7 You awake in the night to find that your living room is on fire. Your one chance to save yourself is to throw something that will hit the back of your bedroom door and close it, giving you a few seconds to escape out the window. You happen to have both a sticky ball of clay and a super-bouncy Superball next to your bed, both the same size and same mass. You ve only time to throw one. Which will it be? Your life depends on making the right choice! A. Throw the Superball. B. Throw the ball of clay. C. It doesn t matter. Throw either. Larger p more impulse to door 2015 Pearson Education, Inc. Slide 9-19

Impulse, Momentum & Collisions Scenarios: One car moving, one at rest Both cars moving in same direction with outside car moving faster (rear collision) Both cars moving toward each other (head on collision) Do all scenarios for: Cars of equal mass AND unequal mass Velcro sides together Magnet sides together In Lab Notebook Record: Scenario (total of 12) Observations in terms of change in velocities of each car

Impulse & Momentum in a Collision A v A v B B -F BonA t F AonB t B During a collision: The forces between the masses are equal but opposite (Newton s 3 rd Law) Time of interaction also same Hence: Impulse same for each F AonB t = -F BonA t v A A B v B p B = - p A Rearranging: p ia + p ib = p fa + p fb

Conservation of Momentum The total momentum of an isolated system does not change. An isolated system is a system with no net external force acting on it External forces are forces from agents outside the system and can change the momentum of the system.

It Depends on the System The goal is to choose a system where momentum will be conserved. For a skateboarder, if we choose just the person, there is a net force on the system. If we choose the system to be the person and the cart, the net force is zero and the momentum is conserved. 2015 Pearson Education, Inc. Slide 9-23

Explosions An explosion is when the particles of the system move apart after a brief, intense interaction. An explosion is the opposite of a collision. The forces are internal forces total momentum is conserved. Initial & final momentum must equal zero Slide 9-24

An 87-kg skater B collides with a 22-kg skater A initially at rest on ice. They move together after the collision at 2.4 m/s. Find the velocity of the skater B before the collision. v A = 0 v B =? 22 kg 87 kg A B

Inelastic Collisions A perfectly inelastic collision is a collision in which the two objects stick together and move with a common final velocity. Slide 9-27

Recoil speed of a rifle A 30 g ball is fired from a 1.2 kg spring-loaded toy rifle with a speed of 15 m/s. What is the recoil speed of the rifle? NOTE: As the ball moves down the barrel, there are complicated forces exerted on the ball and on the rifle. However, if we take the system to be the ball rifle, these are internal forces that do not change the total momentum. 2015 Pearson Education, Inc. Slide 9-28

QuickCheck 9.10 The two boxes are on a frictionless surface. They had been sitting together at rest, but an explosion between them has just pushed them apart. How fast is the 2-kg box going? A. 1 m/s B. 2 m/s C. 4 m/s D. 8 m/s E. There s not enough information to tell. 2015 Pearson Education, Inc. Slide 9-30

Collision and Momentum in 2 Dimensions When collisions occur in two dimensions, we must solve for each component p ix = p fx p iy = p fy In this example, the initial momentum is from m 1 and all in x-direction. After collision the momentum of both balls in x-direction must add to equal the initial momentum The momentum of the balls in the y-direction must cancel (because no initial momentum in y-direction) Slide 9-31

2 pool balls, each of mass 200 g collide as shown below. Calculate the momentum of the white ball after the collision Slide 9-32

Two pucks of equal mass 100 g collide on an air hockey table. Neglect friction. Prior to the collision, puck 1 travels in a direction that can be considered the +x-axis at 1 m/s, and puck 2 travels in the y-direction at 2 m/s prior to the collision. After the collision, puck 2 travels 30 degrees above the +x-direction (between +x and +y) at 0.8 m/s. What is the velocity (direction and speed) of puck 1 after the collision? Slide 9-33