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After this activity, students should be able to:

• Understand that momentum depends on both mass and velocity.
• Explain the difference between an elastic and inelastic collision.
• Recognize that different surfaces and materials promote different types of collisions.
• Collect data to solve equations.
• Apply this information to topics and activities they are familiar with and can relate to from their everyday lives.

Momentum can be thought of as mass in motion and is given by the expression:

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.

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." 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.

In an inelastic collision, momentum is not conserved and the 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 momentum. 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 (see Figure 1).

Figure 1. The illustration of the percentage of energy returned to a ball after one bounce (or, the "range of bounciness" of each ball). click for copyright

In order to complete this activity, you will also need to have an understanding of the motion of an object. Following are the Kinematics equations:

Where d is the displacement of an object, Vi is the initial velocity of the object, Vf is the final velocity, a is the acceleration of the object, and t is the interval of time the object traveled. For example, if a ball is rolled off of a table 1 meter above the ground, we can find the velocity with which it hits the floor and the time it takes to do so:

If we have three known values, then we must choose equations that use the three values that actually we do have to find the ones that we do not. You also have to read between the lines sometimes to get three known values. For example, in the problem stated previously, the value of acceleration is not given but the object is in free fall, meaning its acceleration is that of gravity.

This activity is best done in groups, because while one person drops the ball, another person must watch the ball and meter stick to note how high the ball bounces. Additional team members could hold the meter stick steady and/or record the data. It is difficult to get an accurate measurement for how high the ball bounces since it is in constant motion. Therefore, have students drop each ball on each surface several times, or until they have a consistent measurement.

Some balls are greatly affected by wind resistance, such as wiffle balls. Therefore, try to pick balls that will not have much influence from wind resistance since this experiment is done under the assumption there exists no wind resistance.

If students have never seen the kinematics equations, this can be a good introduction. Help the students figure out the exact equations they will need to use and walk them through the parts of the worksheets that involve the kinematics equations.

Students could investigate the materials used to make balls as a way to better understand why they bounce the way they do. For example, if you cut open a golf ball, you will find a mass of rubber bands wound around a core that is also usually rubber. All that rubber (and the hard plastic cover) explains its bounciness. A baseball has a similar construction, but with very different materials. A baseball's inside is a mass of yarn wound around a cork core, and its cover material is leather. These materials make for a less bouncy ball. (Note: safety precautions should be taken when opening these balls and should be done under adult supervision.)

The Physics Classroom and Mathsoft Engineering & Education, Inc., 2004, accessed May 30, 2007. http://www.physicsclassroom.com/Class/momentum/momtoc.html

Momentum and energy loss of balls colliding against different surfaces, accessed May 30, 2007. http://www.iit.edu/~smile/ph8709.html

The Exploratorium, Science of Baseball, accessed May 30, 2007. http://www.exploratorium.edu/baseball/index.html

The Exploratorium, Science of Baseball, accessed May 30, 2007. http://www.exploratorium.edu/baseball/howfar7.html

The Exploratorium, Science of Baseball, accessed May 30, 2007. http://www.exploratorium.edu/baseball/howfar5.html