# Momentum and Collisions

## Demonstration Kit

### Introduction

Which collision will impart more momentum—an object that hits a door and sticks to it, or an object that bounces straight back from the door? Use this simple demonstration to clearly show the effects of bouncing and recoiling, and to distinguish between inelastic and elastic collisions.

### Concepts

• Conservation of momentum
• Conservation of kinetic energy
• Inelastic vs. elastic collisions
• Recoil

### Materials

Balance, 0.1-g precision
Happy/Sad Balls, with hook screws, 1 pair*
Ring stand with crossbar
Ruler
String, 2 m*
Tape
Wooden blocks, 2*
*Materials included in kit.

### Safety Precautions

The materials in this demonstration are considered nonhazardous.Follow all laboratory safety guidelines.

### Disposal

All materials may be saved and stored for future use.

### Prelab Preparation

1. Set up the ring stand and crossbar as shown in Figure 1.
{12093_Procedure_Figure_1}
2. Cut two one meter lengths of string.
3. Tie a loop knot on one end of each string (see Figure 2).
{12093_Procedure_Figure_2_Loop knot}
4. Using the hook, suspend the happy and sad balls from a loop knot in the string. Attach the strings to the crossbar by wrapping them several times around the crossbar so the balls are at equal heights approximately 8 cm from the ground.
5. Set up the two wooden blocks right in front of both the happy and sad balls, so that the balls are suspended approximately in the center of each block, and just touching each block as they hang (see Figure 1).
6. Practice the procedure before demonstrating in class.

### Procedure

(Optional) If desired, demonstrate the different properties of the happy and sad balls by removing them from their strings and dropping them to the floor, ensuring they do not land hook-first. The happy ball should bounce to nearly its original height, whereas the sad ball should bounce very little, if at all. Reattach the happy/sad balls to their strings.

1. Draw back each ball about 25 cm from the wooden blocks.
2. Ask the class to make predictions about what will happen to the two blocks when the balls are released.
3. Release the balls. Note: The happy ball will bounce off the block and nearly make it to its original height and the block will be knocked over. The sad ball barely rebounds and the block will wobble but not fall.
4. Have the students record observations and speculate on the apparent discrepancy on why one block fell while the other did not.
5. Repeat the demonstration as many times as desired, switching boards to prove the difference is in the balls and incorporating any student suggestions.
6. (Optional) Measure the mass of each ball to show that the happy ball actually weighs slightly less than the sad ball. Mass certainly cannot account for the difference in momentum transfer!

### Student Worksheet PDF

12093_Student1.pdf

### Teacher Tips

• The materials in this kit are completely reusable, and the demonstration may be related an indefinite number of times. The demonstration takes about 10 minutes to perform and serves as a great introduction to the idea of collisions and momentum transfer.
• The Sad Ball may be composed of several different materials. Common materials used are poly(norbornene) and a poly(styrene–butadiene) block copolymer. These materials have a high specific gravity, about 1.17 g/mL, and have low elasticity, and an ability to absorb energy. Thus, when the ball is dropped, it does not bounce. These properties make the Sad Ball material useful for a number of applications. The poly(styrene–butadiene) co-polymer is used in automobile tires where it helps to absorb some of the bumps encountered on the highway. Polynorbornene is used in lining ballistic containers used by bomb squads (these look like big trash cans). Should a bomb explode, the rubber material will absorb a significant amount of energy.
• The Happy Ball is a sphere having an extremely high resiliency factor, in excess of 90%, and a high coefficient of friction. The Happy Ball has a lower specific gravity and is composed of about 100 parts polybutadiene, 0.5 to 15 parts sulfur vulcanizing agent, and 5 to 15 parts of filler such as hydrated silica, carbon black or lithium oxide. The sulfur vulcanizing agent is added in excess to products such as automobile tires (which contain about 3 parts sulfur) to produce cross-linking between the polybutadiene chains. Cross-linking gives the rubber its high resiliency. The ball is molded at a pressure of between 500 and 3,000 psi for 10 to 30 minutes at a temperature of 285–340 °F (140–171 °C). This produces the Happy Ball with the properties described above. In addition, it has been found that these balls also exhibit an ability to conserve energy. That is, when bounced, the ball will dissipate very little of its initial energy in the form of heat.

### Science & Engineering Practices

Developing and using models
Planning and carrying out investigations
Analyzing and interpreting data
Using mathematics and computational thinking

### Disciplinary Core Ideas

MS-PS2.A: Forces and Motion
HS-PS2.A: Forces and Motion

### Crosscutting Concepts

Cause and effect
Scale, proportion, and quantity
Systems and system models

### Performance Expectations

HS-PS4-1: Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

### Sample Data

Record your observations of the collisions between the different balls and their respective blocks.

One ball bounced back much higher than the other, and knocked the board over. The other ball did not rebound at all and it only caused the board to wobble slightly. The same thing happened even when the boards were switched.

1. What are the characteristics of an elastic collision? An inelastic collision? A completely inelastic collision? Give at least one example of each.

An elastic collision conserves kinetic energy, whereas inelastic and completely inelastic collisions do not. Most real world collisions will always be partially inelastic as there will be some energy lost due to sound, heat, deformation, etc. A close approximation of an elastic collision would be bouncing a rubber superball against a wall. An inelastic collision would be throwing a snowball against a wall, because energy is lost due to deformation. A completely inelastic collision would be throwing a dart against a dartboard, because it would then stick.

2. Is total momentum conserved in each type of collision? Is kinetic energy conserved? Is total energy conserved? Explain.

Momentum is conserved in each type of collision, as is total energy. Kinetic energy, however, is lost in an inelastic collision as some (or all) of the energy is transformed into other types of energy.

3. Why did one ball knock the block over and the other did not? What would happen if the happy/sad balls were allowed to fall from a greater height?

Because the happy ball bounced straight back, it transferred more momentum than the non-bouncing sad ball, which did not transfer as much momentum and absorbed some of the kinetic energy. If the happy/sad balls were allowed to fall from a greater height, the sad ball would transfer enough momentum to tip the block.

### Discussion

When an object is in motion, it has a property known as momentum. It is a vector, which means its unit defines a quantity and a direction. Momentum (p) is calculated by multiplying the mass (m) of the object by its velocity (v); p = mv. A fundamental principle of physics is that the momentum of an isolated system of objects always remains constant. This is known as the conservation of momentum. If objects within a system collide, the momentum of each individual object before and after a collision may change, but the total momentum of the system will remain constant.

There are two types of collisions—elastic and inelastic. An elastic collision occurs when the total kinetic energy of a system is conserved. Examples include colliding billiard balls and gas molecules. An inelastic collision occurs when the total kinetic energy of a system is not conserved. Note that the total energy is conserved; however, some energy may be lost due to deformation, sound or heat. A martial artist breaking a board would be an example of an inelastic collision, as energy would be lost due to deformation. A completely inelastic collision is when the two objects stick together and move as one after a collision. This involves the greatest kinetic energy lost. An example of a completely inelastic collision is when a baseball hits the catcher’s mitt and stops. In every collision, elastic or inelastic, momentum is always conserved. The main difference between the two types of collisions is that for an elastic collision, the kinetic energy of the system also remains the same. The conservation of energy principle does not apply to an inelastic collision because in an inelastic collision much of the energy is lost as heat and sound by the frictional forces that arise when the objects deform and “stick” together.

Total momentum is conserved. The general equation to show momentum before and after a collision with a stationary object—which has no initial momentum—is seen in Equation 1.

{12093_Discussion_Equation_1}
In the case of the Sad Ball, it ceases moving forward once it has struck the board. Thus, Equation 1 simplifies to Equation 2.
{12093_Discussion_Equation_2}
Where the final momentum of the board is equal to the initial momentum of the ball.

In the case of the Happy Ball, the ball rebounds off the board with an approximately equal velocity, in the opposite direction. Equation 1 then becomes:
{12093_Discussion_Equation_3}
Thus, we find the final momentum of the board to be

2mballvball = mboardvboard,f

The board has had twice as much momentum transferred to it with the Happy Ball as opposed to the Sad Ball. This difference is enough to “tip the edge,” and knock the board over.

### References

Flinn Scientific saw this activity demonstrated for the first time by Jeremy Lederhouse, then a graduate student at Northern Illinois University, for the Spooky Science Saturday, October 2009.

Halliday, D., Resnick, R., Walker, J. Fundamentals of Physics, 7th ed. John Wiley & Sons, Inc.: DeKalb, IL, 2005; pp 217–23.

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