Exercise 2: Collecting data
For this experiment you will need to collect the following items:
- bouncy ball (small rubber one, basketball, volleyball, soccer ball…)
- measuring tape
- phone to record audio track
- a device which can use an audio visualiser (Audacity, etc)
- a towel or something similar to make the floor “softer”
Prodecure:
The following experiment will be performed twice. You will use the same ball both times, but change the “ground” material. In the first experiment, use a smooth, flat, hard surface (countertop, a dense table, hard floor, etc). In the second experiment, use a piece of cardboard or cloth (t-shirt, tea towel, etc) on top of your smooth, hard surface.
Measure a height of about 1 m above the surface you will be using in your experiment.
Record an audio track that captures the collisions and bouncing of your ball (see the instructions “Finding the time between impacts” below). You will be using the length of time between collisions (bounce time) to calculate the energy loss, so be sure you are able to collect precise data.
Using your recording, obtain the time at which each collision happened and record it in the table of results. Try to measure at least eight bounces (nine collisions with the ground).
Repeat the experiment for the second ground material. Try to measure at least five bounces (six collisions with the ground). You should notice that on the hard surface there are more bounces and the ball bounces higher than on a soft surface (i.e. with the cardboard or cloth layer). You will already realize that this is because the ball loses more mechanical energy on the soft surface than on the hard surface. The collision on the hard surface is closer to a perfect elastic collision.
Notes: you should be filling in the first two columns of the results table with your waveform data. The last two columns, (v0, and K/m) will be calculated in the next section.
Finding the time between collisions
In Lab 1, you used a video recording to make precise height measurements. In this lab, we are concerned with the time between collision with the ground, and in fact don’t need to see the ball at all. This allows you to use an audio recording to obtain very precise data. Just like video, an audio recording can be thought of as a series of sound “snapshots”. That is, digital audio recordings are not “continuous” and are made of many tiny audio “samples” taken over short periods of time. You can think of a single sample as a single frame. When all of the samples are played back-to-back, you will hear an accurate reproduction of the real sound (provided enough samples are taken per second).
As described in Lab 1, your phone camera likely records about 30 frames per second when taking a video. On the other hand, audio is sampled at a much higher rate. This is for physiological reasons (the human eye can process about 10-12 frames per second as separate images – everything else appears as motion) as well as technical reasons (images require much more storage than audio). However, audio requires a much higher sampling rate to sound realistic. For this reason you should be able to determine with a high level of precision when the ball makes contact with the ground by looking for peaks in your recording which correspond to the sound of your ball colliding with the ground.
There are a variety of ways to visualize your audio track’s “waveform” outlined in the appendix.
An example of a waveform with 3 “collisions” and 2 “bounces” is shown in Figure 2.1 below. Now you can use the spacing between “peaks” to determine ∆t!
Exercise 2.1 (2 marks)
i) Submit a photo of your experimental setup and ii) a screenshot of your audio waveform.
| Surface 1: _________ | Surface 2: _________ | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Collision # | Time (s) |
Time between collisions, Δt (s) |
v0 (m/s) |
K / m = ½ v02 (J/kg) |
Collision # | Time (s) |
Time between collisions, Δt (s) |
v0 (m/s) |
K / m = ½ v02 (J/kg) |
| 1 | 1 | ||||||||
| 2 | 2 | ||||||||
| 3 | 3 | ||||||||
| 4 | 4 | ||||||||
| 5 | 5 | ||||||||
| 6 | 6 | ||||||||
| 7 | 7 | ||||||||
| 8 | 8 | ||||||||
| 9 | 9 | ||||||||
| 10 | 10 | ||||||||
| 11 | 11 | ||||||||
| 12 | 12 |
Now that you know how long the ball is in the air between collisons, you can use the equation you derived in (1.2) to calculate the speed of the ball as it leaves the ground, v0. Then, you can use this speed to calculate the kinetic energy of the ball as it leaves the ground for each bounce, 
. However, you’ll notice we have asked you to calculate K / m. This is for a few reasons. First, since you use the same ball for all experiments, so mass, m is a constant throughout the lab. This means that if K changes by some amount, we know the change represents a change in speed only. Additionally, since we don’t know the exact value of m, dividing K by m means you can obtain a numerical result that does not depend on m.
Exercise 2.2 (4 marks)
Calculate v0 and K/m, then fill in the next two columns of your chart. Submit your completed charts for both surfaces.
Note: you will not be able to get as many bounces with the soft surface as with the hard surface, this is okay. Aim to get at least 5-6 with the soft surface and 9-10 with the hard surface (more is better).
Before you continue!
Before continuing, be sure you have completed (2.1) and (2.2), which will be graded and submitted through Crowdmark.
