HANDS-ON ACTIVITY: BOUNCING BALLS CONTRIBUTED BY: INTEGRATED TEACHING AND LEARNING PROGRAM AND LABORATORY, UNIVERSITY OF COLORADO AT BOULDER

KEYWORDS energy, momentum, collisio n, elastic, inelastic, potential energy, kinetic energy, conservation of momentum energymomentumcollisio nelasticinelasticpotential energykinetic energyconservation of momentum

LEARNING OBJECTIVES Understand that momentum depends on both mass and velocity. Recognize that difference surfaces and materials promote different types of collisions. Collect data to solve equations.

MATERIALS LIST 3 different balls: Ping Pong, Golf, Tennis 3 different bouncing surfaces: Smooth side of Brick, Table, Cork Floor Electronic Scale Meter stick

PRE-ACTIVITY ASSESSMENT Brainstorming: What are sports examples of transfer (and conservation) of momentum?

INTRODUCTION Momentum can be thought of as 'mass in motion' and is given by the expression: Momentum = mass x velocity The amount of momentum an object has depends both on its mass and how fast it is going. For example, a heavier object going the same speed as a lighter object would have greater momentum.

Sometimes when moving objects collide into each other, momentum can be transferred from one object to another. There are two types of collisions that relate to momentum: elastic and inelastic.

ELASTIC COLLISIONS An elastic collision follows the Law of Conservation of Momentum, which states "the total amount of momentum before a collision is equal to the total amount of momentum after a collision." In addition, the total kinetic energy of the system (all the objects that collide) is conserved during an elastic collision.

An elastic collision example might involve a super- bouncy ball; if you were to drop it, it would bounce all the way back up to the original height from which it was dropped. Another elastic collision example may be observed in a game of pool. Watch a moving cue ball hit a resting pool ball. At impact, the cue ball stops, but transfers all of its momentum to the other ball, resulting in the hit ball rolling with the initial speed of the cue ball.

INELASTIC COLLISION In an inelastic collision, the total momentum of the system is conserved, but the total kinetic energy of the system is not conserved. Instead, the kinetic energy is transferred to another kind of energy such as heat or internal energy. A dropped ball of clay demonstrates an extremely inelastic collision.

It does not bounce at all and loses its kinetic energy. Instead, all the energy goes into deforming the ball into a flat blob. In the real world, there are no purely elastic or inelastic collisions.

Rubber balls, pool balls (hitting each other), and ping-pong balls may be assumed extremely elastic, but there is still some bit of inelasticity in their collisions. If there were not, rubber balls would bounce forever. The degree to which something is elastic or inelastic is dependent on the material of the object.

PROCEDURE Determine the mass in kilograms of each ball and record it on the data sheet. Drop each ball from a distance of 1 meter onto the surface and record how high it bounces in meters (Example:.46 meters).

Note whether the ball and surface showed more of an elastic or inelastic collision. If the ball bounces up more than.5 meter then, it is more elastic. If it bounces up less than.5 meter, then it is more inelastic. Repeat steps 1, 2 and 3 for the two other surfaces

Calculate the momentum for each ball at the point that it bounces, and record on the worksheet. Do one example calculation as a class. Note: The momentum calculation is independent of the bouncing surface, so it only needs to be calculated once for each ball. Equation: Momentum = mass x velocity

Use the mass determined in step 1. In this example, use.05 kilograms for the mass. Next, determine the velocity of the object when it hits the ground. Velocity of a falling object can be described as: where g is gravity (9.81 m/s 2 ) and h is height (1 m).

POST-ACTIVITY ASSESSMENT Graphing: Make two separate bar graphs—one for momentum and one for velocity. Put the surface type on the x-axis, and the velocity and momentum on the y-axis (for each respective graph). Then make three different colored plots on each graph representing the different ball types. Use these graphs to visually represent which balls had the most elastic collisions and on which surface they occurred.

MOMENTUM = MASS X VELOCITY Problem Solving: Calculate which case has the greater momentum. Case 1: A big-time slugger hits a 0.14 kilogram (5 ounce) baseball 45 meters/sec (100 mph). Case 2: Uncle bill knocks down four pins at the Bowl-a-Rena by rolling a 7.3 kilogram (16 pound) ball 4.5 meters/sec (10 mph).