University of Virginia
Physics Department

## Galileo's Gravitational Experiment

A Physical Science Activity

2003 Virginia SOLs

• PS.1
• PS.10

Objectives

Students will

• understand the relationship between gravitational force, mass, and acceleration;
• study the motion of freely falling objects.

Motivation for Learning

Discrepant Event: Tennis Ball vs. Paper

Materials
• Tennis Ball
• 1 Sheet Notebook Paper (8"x11")

Procedure

1. Hold the tennis ball and notebook paper (horizontally) the same distance from the ground. Ask the students which would strike the ground first if both were dropped. They will likely choose the tennis ball.
2. Drop both objects and observe. The tennis ball should strike first.
3. Ask the class why the paper fell at a slower rate than the tennis ball. Ask for suggestions on how to make the paper fall faster.
4. Crumple the paper into a ball. Drop the paper and tennis ball again. This time, both should reach the floor at about the same time.
5. Ask the class to explain the difference.

Background Information

If a bowling ball and tennis ball were dropped from the same height, which would strike the ground first? Does the mass of an object affect its acceleration due to gravity? These were concepts that Galileo Galilei sought to understand through a series of experiments that studied acceleration. Because he lacked a suitable timing device, Galileo used an inclined plane to slow the motion of the objects. As the angle of the plane with the ground increased, so did the component of the gravitational force, and therefore the acceleration. He found that the acceleration of an object was constant over time, regardless of its mass. Therefore, a bowling ball and tennis ball would both reach the ground at the same moment. This concept is demonstrated in the Discrepant Event, by comparing a tennis ball and a sheet of paper. In the absence of air resistance, both should reach the ground at the same time regardless of their shape. Crumpling the paper into a ball reduces the resistance and demonstrates a constant gravitational acceleration.

All objects near the surface of the Earth fall with the same acceleration, 9.8 m/s2. This means that if an object were dropped from rest, after one second it would have a velocity of 9.8 m/s, after two seconds its velocity would be 19.6 m/s, and so forth. There are two parts to this experiment. In the first part, the students will replicate Galileo's original experiment, using an inclined plane to measure the acceleration of an object. Only one object, a marble, will be used in this part, so the mass will remain constant. The students will view the impact of a greater angle of inclination on the acceleration of the marble.

The second part of the experiment can vary slightly. This portion involves a student dropping various balls from a specific height to study their motion in free fall. The results will be more accurate from a greater height. One possibility would be to drop the balls from the classroom window to another student waiting below, outside. However, care should be taken to ensure that the outside area is clear of other people. Another option is to release the balls from a surface within the classroom, such as a lab bench or table top. Select something that works best for your situation, but still provides a great enough distance so that acceleration can be measured.

After the experiment, the students are asked to make a few calculations. They should understand the relationship between distance, time, velocity and acceleration to make these calculations. For a body starting from rest moving under constant acceleration, the velocity is given by v2 = 2ad where a is the acceleration and d is the distance traveled.. For free fall, a is the acceleration of gravity labeled by g, g =9.8 m/s 2, and d is the distance the body falls.  The velocity v is given by . For a body moving down the inclined plane, the acceleration down a plane placed at an angle θ from the horizontal should be given by gsinθ. The velocity of a body moving under constant acceleration a for a given time t starting from rest is given by v = at.

### Student Activity

Materials

 Protractor Golf ball Stopwatch Tennis ball Marble Basketball Meter stick Baseball Styrofoam ball Wooden board (2 m long) with a recessed groove to fit the marble, or a plastic car racetrack with raised edges

Procedure

Part 1

1. Lay the wooden board on the table. Using the protractor to measure the angle, raise the board 5° from the table. Appoint one partner to hold the board and release the marble, and another to act as a timer.
2. Place the marble in the groove at the top of the board and release. Use the stopwatch to record the time it takes for the marble to reach the bottom. Record this in the data table.
3. Using the protractor, raise the board to 10° from the table. Release the marble from the top, and record the time.
4. Repeat this procedure for the following angles: 15°, 20°, 25° and 30°. Record your results.

Part 2

1. Station one member of your group at a surface at least 2 m from the ground; the higher the distance, the better (ask your teacher for specific instructions).
2. Station a second member on the ground directly below with a stopwatch.
3. From the high surface, release the golf ball. Record the time it takes for it to reach the ground.
4. Repeat this with the tennis ball, basketball, baseball and Styrofoam ball. Record your results on the data table.

Data Sheet

Part I:

 Angle Distance Time (seconds) Final velocity Initial Velocity Acceleration (Final velocity/time) 5° 0 m/s 10° 0 m/s 15° 0 m/s 20° 0 m/s 25° 0 m/s 30° 0 m/s

Part 2:
 Type of Ball Distance (m) Time (s) Final Velocity Acceleration (Final Velocity/time)

Questions

1. What relationship did you find in Part I between the acceleration of the ball and the angle of the wooden board? Explain this in terms of the gravitational force.

2. In Part II, did all of the balls reach the ground in approximately the same time? Were their acceleration values comparable? Explain.

3. How did the results for the Styrofoam ball compare to the others? Can you account for this difference?

Students with Special Needs

All students should be able to participate in this activity.

Click here for further information on laboratories with students with special needs.

Assessment

Data sheet to be completed during the laboratory.