# Measuring "g" - Time of Fall Method

(Data Table)

## Purpose:

To measure the acceleration of free fall, "g."

## Discussion:

We have said that if you drop an object from rest the distance the object falls, d, is related to the time, t, by:

where t is the time that it takes to fall the distance d. Solving for g gives:

Therefore, it is theoretically straightforward to determine the acceleration of free fall simply by dropping something and measuring the time it takes to hit the ground.

Experimentally, however, it is exceedingly difficult to get precise-enough times for meaningful results. (It often turns out that the theoretically straightforward approach is exceedingly impractical in the "real world.") Over short distances (and short times), human reaction time destroys the precision of the measurement, and over long distances, air resistance becomes a factor so that the acceleration of the object is no longer constant and the calculation is invalid. These considerations (among others) are what forced Galileo to develop his famous inclined plane experiment.

The Pasco Free-Fall Adapter gives us the technology to obtain precision timing for objects dropped relatively short distances, however. When the ball is dropped, it activates a switch to start a very accurate timer. When the ball strikes the pad at the end of its fall, it trips another switch to stop the timer. Simple and straightforward!

## Pasco Science WorkshopTM interface free-fall adapter meter stick/metric tape metal sphere ring stand ring stand clamp C-clamp Setting Up:

The apparatus will be set up for you.

## Procedure:

1. Adjust the height of the free-fall adapter to some new height (your choice) using the clamp on the ring stand.
2. Line up the free-fall adapter so that the sphere hits the floor switch when it is released.
3. Measure the height that the ball will fall from the adapter to the floor switch. Record this measurement in your data table.
4. If the button in the control bar at the top of the window says "Start", click it. If it says "Stop," leave it alone. You do not need to start or stop the interface between runs.
5. To put the sphere in the apparatus:
1. Place the ball between the metal contact and the metal bar. (See the image at right.)
2. While holding the ball in place, push the metal rod and tighten the thumb screw to hold the ball in place without your assistance. DO NOT OVER-TIGHTEN THE THUMB SCREW!
6. To release the ball, CAREFULLY loosen the thumb screw.
7. Read the time of fall from the digital display, and record this value in your data table.
8. Repeat steps 5 - 7.

## Results:

1. Calculate the mean (average) time and record it in your data table.
2. Use your average time and height to calculate a value for "g." Show your calculation.
3. Your teacher will tell you how to share your value with the class.

## Conclusions:

The conclusions for this lab are on the data sheet.

last update August 28, 2009 by JL Stanbrough