## Demonstration goals:

- Explain how the acceleration of gravity gives a planet’s mass
- Measure the acceleration of gravity using the ball-drop method
- Understand the limitations of this method
- Measure acceleration of gravity using the period of a pendulum
- Understand the limitations of this method

### Measuring gravity using the ball-drop method

Perhaps the most famous of Galileo‘s experiments involved dropping two balls from a great height. (In actuality, he never dropped anything from the Leaning Tower of Pisa; instead, he had them dropped from the crow’s nest at the top of a sailing ship.)

To replicate his experiment, you will need:

- Ball drop apparatus (Fisher VBS40881-1 $40.0 and VBS40990-1 $339.00)
- 2 Balls, of roughly the same size, but different weights
- Table or other flat, hard surface

1. Set up the Ball Drop apparatus before class. Double-check to make certain that the battery is charged, and that the room is dark enough for the IR sensors to work.

2. Pass the balls around the class. Have the students predict which ball will hit the ground first, the heavier or the lighter, and record their predictions on the blackboard.

3. Hold the balls in one hand, at a height of at least one meter over the table. Release the balls, and note the simultaneous noise of the impact. Point out that (to a first-approximation) the weight of the ball does not affect the rate at which it falls.

Now let’s go Galileo one better!

4. Place the small plastic ball that came with the ball drop apparatus. Show that the acceleration due to gravity can be found from the difference in velocities, as measured at the two IR sensors. Release the ball, and record the times one the board. Calculate the acceleration using:

_{1}– t

_{2})/(t

_{1}*t

_{2}*t

_{12})

where d is the diameter of the ball, t_{1} is the time the ball takes to pass through the first gate, t_{2} is the time the ball takes to passthrough the second gate and t_{12}is the time the ball takes to pass between gates.

5. Repeat with the steel ball, and compare the results.

**For Discussion:**

How well do your measurements agree with the accepted value of ~9.78 m/s/s? Why do you think the difference in the times between the two balls exists? (HINT: Think friction!)

### Measuring gravity with a pendulum

One day, while attending a Mass in the Duomo di Pisa, Galileo noticed that the lamp above him was swaying slowly. The slow, regular motion of the lamp inspired Galileo to check the measurements for gravity (which he had previously done using the inclined plane) by using the well known formula for the period of a pendulum: t = 2 pi sqrt (L / g) where L is the length of the pendulum. For this experiment, you will need:

- A Stopwatch
- A pendulum (Fisher CHS41475 $51)
*Alternative:*Make a pendulum using 1.5 m of string, a lead fishing weight and a ring-stand apparatus (or equivalent)

1. Set the pendulum length at .5 m.

2. Time how long the pendulum takes to make 10 oscillations.

3. Using the formula given above, calculate the gravity.

4. Now set the pendulum length to .75 m and repeat the experiment. Once again, calculate the gravity.

**For Discussion:**

How well do your measurements agree with the accepted value of ~9.78 m/s/s? How well do the two values compare? What may have caused the difference in the two values? (HINT: Think about the effect of pendulum length on the period.)

**Related pages:**

- The Galileo Project (A guided tour of Galileo’s life)
- Il Museo della Storia delle Scienze, Firenze (A science museum in Florence with many artifacts from Galileo)