Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Twist the needle into the end of the hand pump.
2. Using the hand pump, inflate the eight miniature basketballs.

Safety Precautions

Wear safety glasses or chemical splash goggles. The goal is to launch the various balls vertically, but the launch direction will be random and may occasionally be at angles or horizontal. Be sure nearby students are wearing eye protection before performing the double-ball drop.

Disposal

The materials should be saved and stored for future use.

Lab Hints

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. All materials are reusable. This laboratory activity can reasonably be completed in one 50-minute class period. To keep the cost of this kit as low as possible, only enough mini basketballs and large rubber balls are included to be shared between the 15 groups. Eight groups can work with the mini basketballs while the other seven groups work with the large rubber balls and vice versa. For the large rubber ball-mini basketball double-drops, two groups can work together to collect data.
• Some basketballs may be flatter than others. This will reinforce the important properties involved in this conservation of energy and momentum experiment.
• The top (launched) ball will not travel even close to the theoretical height of 180 cm (when dropped from 20 cm), due to internal friction in the balls and imperfect elastic collisions. However, students should recognize that different ball combinations work better than others. Students should be able to evaluate the different ball combinations and determine what characteristics make one combination better than another.
• Make sure students hold the balls vertically above each other and nearly touching. Students should practice their release technique several times before beginning the data collection process.

Teacher Tips

• The equation for the speed of the small (top) ball (m₂) can be determined using the conservation of momentum and conservation of kinetic energy expressions (Equations 1 and 2). Equations 1 and 2 are used to derive Equation 3, after some very lengthy algebra. It can be seen from Equation 3 that as m₂ approaches zero (0), the final velocity of m₂ approaches 3v_i.
  {13094_Tips_Figure_4}
  {13094_Tips_Equation_1}
  {13094_Tips_Equation_2}
  {13094_Tips_Equation_3}
• Demonstrate a triple-ball drop using the large rubber ball on the bottom, small rubber ball in the middle and the Ping Pong ball as the top ball. Or use a regular-size basketball as the bottom ball and a tennis or racquet ball as the middle ball. The theoretical height should be 81 times the drop height! Use extreme caution when performing this demonstration—the top ball can fly anywhere. All students should wear safety glasses during this demonstration.
• To obtain the best height, the two dropped balls must be close to, but not touching, each other as the Bottom Ball collides with the ground.

Sample Data

Answers to Questions

1. Calculate the average Maximum Rebound Height and Launch Height of the top ball for each experiment. Record these values in Data Tables 1 and 2, respectively.

   See Data Tables 1 and 2.

2. Describe what happened to the top ball during the double-ball drop experiment.

   Nearly every top ball shot up much farther during the double-ball drop compared to the single ball drop. Many times the top ball was “lost” when it launched in a horizontal direction. The top ball traveled a great distance.

3. Describe what happened to the bottom ball during the double-ball drop experiment.

   The bottom ball barely moved after the collision with the floor. It rebounded not more than a centimeter as the top ball flew up to a great height.

4. Compare the initial rebound heights (Data Table 1) to the double-ball drop rebound heights for each top ball. Relative to the initial rebound height, which ball performed the best as the top ball?

   Each ball that acted as the “top ball” traveled to a rebound height much greater than the initial single ball-drop rebound height. The small rubber ball launched to the greatest average height (86 cm) when the large rubber ball was the bottom ball. The Ping Pong ball had the highest single launch (90 cm) when used with the basketball. However, the marble had the largest increase in height compared to the single-ball drop rebound height. The marble only bounced to 8 cm when it was dropped by itself. When the marble was used as the top ball, it shot up to 73 cm when used with the basketball and 85 cm when the large rubber ball was the bottom ball.

5. Which top ball launched to the greatest height?

   The Ping Pong ball launched to the greatest single trial height (90 cm) when used with the basketball. However, the small rubber ball had the greatest average height (86 cm) when used with the large rubber ball.

6. Which top ball launched to the lowest height?

   Using the basketball on top of the large rubber ball, or the large rubber ball on top of the basketball both produced equally poor results. Both launched to an average height around 24 cm.

7. (Optional) Which bottom ball performed the best as a top ball launcher?

   The large rubber ball performed the best as the bottom ball. Except for the Ping Pong ball, the large rubber ball launched all the balls to greater average heights.

8. (Optional) What double-ball drop combination resulted in the greatest maximum height of the top ball?

   The large rubber ball and small rubber ball was the best double-ball drop combination, resulting in an average top ball height of 86 cm.

9. Explain some possible sources of error for why the top ball did not launch to the theoretical height of nine times the drop height.

   In order for the top ball to launch to nine times the original drop height, perfectly elastic collisions must occur. No energy may be lost to friction, heat, or sound during the compression of the balls. However, this naturally occurs with the balls used in this lab. The mini basketball was very flexible and a lot of energy was lost as it compressed during the collisions. However, it still worked well as a bottom ball. Also, many times the top ball did not launch straight up so the height measurement was not accurate—it was more of an estimation. The series of collisions must also be just right to generate the best energy transfer. This occurs when the top ball and bottom ball are separated by only a few millimeters as they fall. When they are directly in contact or too far apart, the greatest amount of energy is not transferred into the top ball.

Introduction

When a vertically positioned two-ball system is dropped, how will the balls respond after colliding with the floor, and with each other? The results might surprise you. Experiment with the “two-ball drop” and determine the factors that cause one ball to rebound much higher than its original starting height.

Concepts

• Collisions
• Conservation of momentum
• Conservation of energy
• Elasticity

Background

When an object is set in motion, the object has a property known as momentum. 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 the individual objects 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 objects collide and then separate after the collision. An example of an elastic collision is the collision between a baseball and a bat. An inelastic collision is when objects collide, stick together, and move as one object after the collision. An example of an inelastic collision is when the 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. Kinetic energy (KE) is calculated by multiplying one-half the mass (m) by the velocity (v) squared; KE = ½ mv². 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 due to frictional forces that arise when the objects deform and “stick” together.

In this activity, elastic collisions occur between the falling balls because the two balls move as two separate objects before and after the collision. Since the double-ball drop results in an elastic collision, both the conservation of momentum and the conservation of kinetic energy principles apply.

To clearly visualize the observed results of the collisions, three events must be described—the initial ball drop, the collisions and the rebound. (Refer to Figures 1a–1c during the following explanation.)

In the initial drop (Figures 1a and 2a), the balls are released and fall to the ground with the same acceleration. The two balls are nearly touching as they fall. The instant before the bottom ball (Ball A) hits the ground, the two balls will have the same downward speed. The first collision occurs when Ball A hits the ground. To conserve energy and momentum during this elastic collision, the collision between Ball A and the stationary ground causes Ball A to bounce upward with the same speed it had just before hitting the ground. Because of the small separation between the top ball (Ball B) and Ball A, for a brief instant, Ball B continues to fall downward as Ball A bounces upward—with equal but opposite speeds.

The second collision (Figures 1b and 2b) occurs between Ball A traveling up and Ball B traveling down. The collision between Balls A and B is equivalent to a head-on collision of two objects with the same speed (s). Imagine being in the reference frame of Ball A, in which Ball A does not appear to move. In the reference frame of Ball A, the ground appears to travel away with speed s while Ball B appears to approach with speed 2s. If Ball A is much more massive than Ball B, then Ball A will not lose much momentum or energy during the collision with Ball B. Ball A will continue to travel with (nearly) the same speed after the collision and, therefore, it acts as if it is a stationary object for the approaching Ball B. Therefore, just as in the first collision between Ball A and the stationary floor, Ball B must bounce off Ball A with the same initial speed it had before the collision, in order to conserve energy and momentum. This means that Ball B bounces off Ball A with speed 2s. Now, shift back to the reference frame of an observer on the ground (Figure 1c). In ground-observer’s reference frame, Ball A has speed s moving upward and Ball B will have speed 3s moving upward. Ball B travels up with three times its initial speed! The maximum height the ball will reach is proportional to the square of the upward speed, so Ball B will (theoretically) travel nine times (3²) higher than it would if it simply bounced off the ground!

As an example, a two-ball system is dropped from a height of 30 cm. When the bottom ball is much more massive than the top ball, the theoretical height the top ball will reach after the collision is 270 cm! The actual height the top ball reaches will be lower than this theoretical value. Friction, elasticity, rigidity and other factors will affect how much energy is lost by the system during the collisions. Energy loss will result in a lower post-collision speed and a decreased height for the top ball.

Experiment Overview

During the experiment, several types of balls will be studied for the double-ball drop. The mini basketball and large rubber ball will be the main “bottom” balls used to study the response of the other “top” balls. Other double-ball variations may be tried once the main set of data is taken.

Materials

Safety Precautions

Wear safety glasses or chemical splash goggles. The goal is to launch the various balls vertically, but the launch direction will be random and may occasionally be at angles or horizontal. Be sure nearby students are wearing eye protection before performing the double-ball drop.

Procedure

1. Obtain a support stand, buret clamp and a meter stick.
2. Set up the support stand and meter stick as shown in Figure 3.
   {13094_Procedure_Figure_3}
3. Obtain the various balls.
4. For each ball drop, the release height will be 20 cm from the tabletop to the bottom of the lowest ball.
5. Start with the mini basketball.
6. Line up the bottom of the basketball with the 20-cm mark on the meter stick.
7. Drop the basketball from 20 cm and observe and measure the rebound height. Perform three or four trials and record the highest rebound height of the basketball for each trial in Data Table 1.
8. Repeat steps 6–7 for the four remaining balls.
9. Now, perform the double-ball drop experiments.
10. Obtain the basketball and marble.
11. Hold the marble on top of the basketball as shown in Figure 4. The marble should be nearly touching the basketball. Be sure the centers of the balls are aligned vertically.
    {13094_Procedure_Figure_4}
12. Hold the bottom of the basketball 20 cm above the tabletop.
13. Release both balls at the same time and observe the flight of the rebounding marble.
14. Practice steps 11–13, adjusting the ball holds and ball drop processes accordingly, until the marble launches nearly straight up along the path of the meter stick. It may take four or five attempts to obtain vertical marble rebounds that are repeatable. Note: During practice drops (and all ball drops), be prepared to chase down stray balls that may be launched at random angles.
15. Once two or three vertical rebounds are successfully completed, repeat steps 11–13 to obtain quantifiable data for a total of three to four trials. Measure and record the maximum rebound height of the marble for each “successful” trial in Data Table 2. A “successful” trial is one in which the marble launches nearly straight up along the meter stick. Note: Even after becoming proficient in generating successful vertical rebounds, not every trial will respond as expected. Be patient and work slowly to obtain quality results. Overall, it may take 10 ball drops to obtain three measurable heights.
16. Repeat steps 10–15 for the various top and bottom ball combinations given in Data Table 2. Record at least three quality data trials for each ball combination.
17. Experiment with other ball combinations as directed by the instructor. Record the ball and height data in Data Table 2.
18. Consult with the instructor for proper storage procedures.

Student Worksheet PDF

13094_Student1.pdf