Physics 250 Laboratory: Motion of a Freely Falling Body

(1-D Kinematics) Lab-Specific Goals:

• To determine the acceleration due to gravity by studying the motion of a freely

falling body.

Equipment List:

• Free-fall apparatus (See figure 1)

o Ball release mechanism

o Steel sphere (1.27 cm or 1.91

cm diameter)

o Receptor pad

o Controller box

o Phone jack connector

• Photogate timer

• Table clamp, rod, and horizontal clamp

• Meter stick

• Ball catcher

Introduction: In this experiment you will make measure-ments of distance and time for a freely falling body in order to verify theoretical predictions and to verify the value of g, the acceleration due to gravity. You will analyze the data to determine a functional relationship of distance vs. time and of velocity vs. time, and check this with what you would expect from the theoretical equations. This method is used extensively in scientific work. Figure 1: Free Fall apparatus The equation of distance as a function of time for a freely falling object is described, according to theory, by the equation 21

2( ) i yiy t y v t gt= + + , (1)

where we are picking a coordinate system in which down is the positive direction. In the situation that you will use the object will be dropped from rest (vyi = 0) and the distance that it falls will be measured from the release point (yi = 0). Thus, the equation becomes: 21

2( )y t gt= (2) (We picked a coordinate system with down for the positive direction to make this equation positive instead of negative.) As seen from the functional dependence, if distance vs. time is plotted, the graph is a parabola. If a graph of distance vs. time squared is made then the graph will make another type of function. Activity: Setup- 1. Clamp the ball release mechanism to a lab stand as shown in the diagram below.

Plug the phone jack into the port on the photogate time. The timer should be set to the “gate” mode.

Figure 2: Photogate Control Pad

2. Position the ball receptor plate directly under the ball and inside the ball catcher. 3. Insert one of the steel balls into the release mechanism, pressing on the dowel pin so

that the ball is clamped between the contact screw and the hole in the release plate. Lightly tighten the thumbscrew to lock the ball into position.

Figure 3: Free Fall Release Device

Dowel Pin Thumbscrew

Data Collection - 1. Turn the timer on and set it to “Gate” mode. 2. Tap the receptor pad to reset the Free Fall Timer device. 3. Press the RESET button on the photogate timer to reset the timer 4. Measure the distance y from the bottom of the ball to the top of the receptor pad and

record this value in Table 1. 5. Loosen the thumbscrew to release the ball. It should hit the receptor pad. If not, reset

the timer, reposition the pad, and try again. 6. Read the time on the digital display of the timer and record this time in the

appropriate row and column of Table 1. 7. Press the reset button on the photogate timer, reposition the Free Fall Device to a new

position and repeat steps 3-6. You should do this for no fewer than eight different positions, being sure to get as wide of a variety of positions as the equipment will allow.

8. For each distance, a value for g can be obtained using 21

2( )y t gt= . Once all of the data have been collected, an average value of g can be found and each individual value compared with this average. The deviation from the mean value should be recorded for each data number and the standard deviation from the mean value of g should be computed and entered in the last cell of the table. The last two cells in your table then have your average value of g determined by your experimental data as well as a measure of the spread in the values obtained.

9. On the graph paper provided, plot the data points collected in your experiment. On

the same graph make a smooth plot of the equation 212( )y t gt= using 9.8 m/s2 for g.

10. Next make a plot of y(t) vs t2 on the graph paper provided.

Physics 250 Lab Template: Motion of a Freely Falling Body

(1-D Kinematics) Score: _____ Section #:______ Name:_____________________________ Name:_____________________________ Name: _____________________________ Calculations:

Data:

Data Number

n y(tn) tn tn

2 g

Deviation δg = |g-gmean|

Squares (δg)2

0 0.00 0.00 0.00

1

2

3

4

5

6

7

8

9

10

gmean= Σ(δg)2 =

Average Value for g =

Standard Deviation of the mean

Note: the quantity Σ(δg)2 is called the variance. To find the standard deviation, divide the variance by (N-1), where N is the number of measurements you made (10), and then take the square root. Standard deviation is a common measure of the uncertainty in a measurement. For “normally distributed data”, 68% of the data should be without 1 standard deviation and 95% should be within 1.96 standard deviations.

Analysis: 1. Plot a graph of y(t) vs. t.

2. Plot a graph of y(t) vs. t2.

3. Compare your data points with the theoretical plot in graph of y vs t. How well does your data match the theory?

4. In the graph that was made of y vs. t2, what does the slope of the graph represent?

How well does it compare to the theoretical value for the slope? 5. From your data table, what was the range of values for g that was obtained? Does the

actual value of g fall within this range? Does it fall within one standard deviation of your mean value?

6. Suppose you hold an object motionless about 4 ft. above the ground and then let it fall to the ground without interference. About how long does it take to hit the ground? (Use your equations and compare it to the value found from your y vs. t graph.)