PhysicsLAB: Freefall: Timing a Bouncing Ball

Procedure

For this lab, two students will form a team. The first student will use a stop watch to time the number of seconds between bounces while the second student will be the observer of how high the ball bounces. When the balls is dropped, the student with the stop watch listens for the sound of the first bounce, starts the stop watch, and then listens for the sound of the second bounce, when he immediately stops timing. The second student observes how high the ball bounces against the backdrop of the wall. To assist with calculating the height of the bounce, there are colored strips (green, orange, yellow pink), each 10-cm wide numbered in 6 sets of four. Once the height and hang time for a bounce are recorded in the data chart, we repeat the process for a total of five trials.

The purpose of this lab is to experimentally calculate the acceleration due to gravity. If you examine each bounce, you will notice that the net vertical displacement equals zero. This tells us that the time for the ball to rise to its apex is exactly equal to the time it takes the ball to fall back to the ground. We also know that the instantaneous vertical velocity at the apex equals zero and the height of the apex.

Calculate the acceleration due to gravity by using the kinematics equation s = v_ot + ½at² and isolate the second half of the golf ball's bounce. Since you could only estimate the height of each apex to the nearest 0.05 meters, you should express the value for your experimental “g” to only two decimal places.

v_o = 0
s = -height of bounce
t = ½ (the total time on your stopwatch)

Click on the picture to view a larger image.

For each trial, place the results of your measurements of time and height as well as your calculated experimental value for “g” in the data table provided.

Data Table

	hang time between bounces	height of apex	experimental "g"
Trial	(sec)	(meters)	(m/sec²)

1

2

3

4

5

Conclusions

What is your group's average experimental value for "g" based on all 5 trials?

Using your average experimental value for "g", calculate a percent error against the accepted value for the acceleration due to gravity at sea level, -9.81 m/sec².

Which aspect of the data collection had the least precision: the timing or the ball's height measurement? Support your choice.

How should the ball’s impact velocity when it first strikes the ground at the start of the bounce compare to its final impact velocity when it strikes the ground at the conclusion of the bounce? Support your answer.

Why did the ball not bounce back up to the height from which it was originally released?

The coefficient of restitution is a measure of the speed of separation to the speed of approach in a collision. In our lab, it can be calculated as the ratio of |v_o| for the ball rising to the apex divided by |v_f | for the ball falling from its initial release off the roof.

You are to calculate the coefficient of restitution for the third ball. Use the fact that the ball was originally released from rest off of the roof which was 5.14 meters above the ground. The height of the apex is recorded in your table. For this calculation use the accepted value of the acceleration due to gravity, g = -9.81 m/sec². This coefficient has no units.

Refer to the following information for the next three questions.

Which of the graphs displayed above correctly illustrates the ball’s position vs time between its two impacts with the ground?

Which of the graphs displayed above correctly illustrates the ball’s velocity vs time between its two impacts with the ground?

Which of the graphs displayed above correctly illustrates the acceleration experienced by the ball between its two impacts with the ground?

A team may submit its data report online together. No papers need to be turned in to the one-way box for this lab.