Exercise 2: Ball Drop
For this experiment you will need the following items:
- A measuring device (ideally a measuring tape, but you can tape sheets of paper together and put markings on it as well).
- An object to drop (e.g. a marble, small ball, battery, a grape, or any similar object).
- A video recording device (a smartphone is ideal).
- QuickTime Player, Windows Media Player, Media Player classic, or any program that can view videos frame-by-frame (see the frame-by-frame analysis for help).
Procedure:
Measure a distance of 1.0 m from the floor along a wall. We define the upwards direction as positive. We also place the origin, (position zero; 
), at the floor. In the next step you will be dropping the object from a height of 
m.
Ask yourself the following questions:
- Does it matter if we say down is the positive direction?
- Does it matter if we say the origin is where we drop the object from?
Now, set up your video recording device to capture the object as it falls from 
m to m (see video below). You will need to measure the position of the object as it is falling. In order to do this, you can make marks with some tape at every 0.05 m or 0.1 m, or you can set up a measuring tape to be visible in the video. The markings will enable you to obtain the position of the object in the video as it is dropped. You can review the video example below where Sara marks positions on the wall in the lab using a measuring tape and scotch tape, and drops objects from a height of 1.0 m.
When you play back your video, you may find that the object moves too fast to make a clear position measurement. You will also notice that the time it takes for an object to fall 1 meter is short. However, if you pause the video, you will be able to observe a (possibly blurry) image of your object near one of your markings. Though the images may be blurry, comparing the location of your object to your markings will allow you to make adequate position measurements.
Videos are just a collection of still images taken in quick succession with a constant time between each image. The number of images your camera takes per second is known as the “frame rate” and is reported in frames-per-second (fps). In order to obtain the position of the object as a function of time, you will take advantage of the fact that most cameras record video at a constant frame rate to make your time measurements.
In order to make the measurements you will need to be able to view the video frame-by-frame. This can be done in many ways, depending on the device you are using. See Frame-by-Frame Analysis for details on how to view and analyse videos frame-by-frame.
You will also need to know the frame rate of your video for the analysis. Most smartphones will either display the frame rate before recording, or have the information accessible under the properties of the video. See Frame-by-Frame Analysis: Framerate if you are having difficulties.
Exercise 2.1 (2 marks)
Exercise 2.2 (3 marks)
Use your video to complete the table below (also provided as an excel sheet). “Δframe #” is the frame number starting at 0, t is the time since the drop in seconds (s), and d is the position in meters (m).
Helpful hints: Be sure to report your answers in SI units. You can use the chart provided above, or you can make a new chart on any spreadsheet software you wish to use, or manually on paper, as long as it is clear in the image you submit. Aim to have between 10-20 frames in your table in order to accurately see the trend. Depending on your frame rate, you may not need to record data on each frame.
| Enter the frame rate, f, of your video in units of fps → f = | |||
| Enter the time between frames, τ, in units of seconds → τ = | |||
| Δframe # | t= (Δframe #) x (τ) [s] | ![t^2 [s^2]](https://ecampusontario.pressbooks.pub/app/uploads/quicklatex/quicklatex.com-99962dac56456c2f3b9795a51c99acb6_l3.png "Rendered by QuickLaTeX.com") |
d [m] |
| 0 | 0 | 0 | 1.0 |
| 1 | |||
| 2 | |||
| 3 | |||
Think about it:
Use the data obtained in your chart to make the following two graphs (manually on graph paper or using any plotting/spreadsheet software of your choosing):
i) Graph position of the object, d, as a function of time, t
ii) Graph position of the object, d, as a function of time, 
Have a careful look at Warm-up Exercise 3. In that exercise you used the kinematic equation:
Now think about how this applies to the graphs you made and which one is linear.
Exercise 2.3 (3 marks)
Draw or fit a best fit line to the linear graph (hint: only one of the two graphs you created should be linear) and submit this linear graph with the best fit line included. Only submit the linear graph. There are helpful graphing tips found in the appendix.
Exercise 2.4 (3 marks)
Making sure to include proper units, calculate the slope of:
i) The best fit line to the linear graph
ii) The acceleration of your object during free-fall (acceleration is a vector!)
HINT: the most accurate way to calculate the acceleration is from your linear graph – how does the slope relate to acceleration? It is not equal but it is proportional…
iii) Finally, we know that objects in free fall have an acceleration due to gravity of 9.8 m/s2 [down]. Does the value you obtained agree with this? Why or why not?
Before you continue!
Before continuing, be sure you have completed Exercises 2.1 to 2.4 on Crowdmark for grading.
