# ACCELERATION DUE to GRAVITY I Exp ACCELERATION DUE TO GRAVITY I Exp. #3

(Alward/Harlow web File: "gravity1.doc" 1-20-04)

## Name: ______Partners: ______Section No. ______

Equipment Needed: Free Fall Timer Apparatus, 2-meter pole, Large table clamp, AC adapter,

### Utility Clamp, Buret clamp, Meter Sticks (2), 15 mm/19 mm ball bearings/washers, Ruler

I. THEORY AND PURPOSE

In this investigation the acceleration due to gravity will be measured and compared to g = 9.8 m/s2.
For a body traveling with constant acceleration, its position along the x-axis is given by Equation 1:
x = x0 + v0t + ½ at2 (1)
where x0 and v0 are the initial position and velocity at time t = 0. If the object is dropped from rest (v0 = 0) from an initial height x0 = 0, then its position at any future time t is given by Equation 2:
x = ½ gt2 (2)
where x is measured downward from the initial height at x = x0 = 0, and g is the symbol used instead of a to represent the acceleration caused by the pull of the Earth.
The student will use a timer to record the time of fall from rest (v0 = 0) through a pre-measured distance d. Thus, using the symbol d as the symbol for distance traveled, we have
d = ½ gt2 so g = 2d/t2 (3) /

II. PROCEDURE

1. Set up the Free Fall Timer apparatus as shown in the figure. Don't forget to plug in the AC adapter.

2. Insert the larger (19-mm diameter) steel ball into the release mechanism, pressing in the dowel pin so the ball is clamped between the contact screw and the hole in the release plate. Lightly tighten the thumbscrew to lock the ball in place.

Adjust the altitude of the clamp to about 2 meters, then measure the exact distance between the bottom of the ball and the top of the receptor plate. Record this distance d in the table.

3. Turn on the timer and press the RESET button.

4. Loosen the thumbscrew to release the ball, which should strike the receptor plate on the floor.

5. Read the time on the digital display of the timer. This is the time it took for the ball to fall a distance d. Record this value in Table 1, and repeat the time measurement for a total of four times. Average four times.

6. Use the average value of the fall time in Equation 3 to calculate the value of g; report the calculated value in Table 1.

7. Before changing to a different height, repeat the measurements of time for the smaller ball. Note: the distances d will be 2 millimeters greater for the smaller diameter ball. This distance difference is too small compared to even the shortest distance (50 cm = 500 mm) to worry about. Put the data for the smaller ball in Table 2.

8. Repeat Steps 2-7 for the other heights d shown in the table.

9. Average the seven values of g for each ball and calculate the percentage difference compared to the known value of g, 9.8 m/s2. Percent difference = |gAve - 9.8 m/s2| x 100 % 9.8 m/s2.

Table 1: Large Steel Ball

d approx
m / d
actual
m / t1
s / t2
s / t3
s / t4
s / tave
s / tave2
s2 / g
m/s2
2.00
1.75
1.50
1.25
1.00
0.75
0.50
Average Value: g = m/s2 / Percent Difference: %

Table 2: Small Steel Ball

d approx
m / d
actual
m / t1
s / t2
s / t3
s / t4
s / tave
s / tave2
s2 / g
m/s2
2.00
1.75
1.50
1.25
1.00
0.75
0.50
Average Value: g = m/s2 / Percent Difference: %

III. PLOT DISTANCE VERSUS TIME-SQUARED

Equation 3 predicts that the position of the falling object, x, varies quadratically with respect to time, t, but x varies linearly with respect to t2. Thus, if we plot x versus the average value of t2, we should expect to obtain a straight line with a slope of ½ g.

 Plot d versus tave 2 for the small ball. Then draw the best straight line possible which passes among the data points. Pick two widely separated points (d1, t1 and d2, t2) on the line; record the corresponding rise and run and calculate the slope ½ g , then compute g. Slope Calculation:

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