Air resistance lab coffee filters answers

Terminal Velocity (At-home)

Purpose: Determine the velocity dependence of air resistance by measuring terminal velocity

Theory:

Newton’s First Law states that an object with a net force of zero will either remain at rest

or continue with the same velocity. This can be observed when an object is in free-fall and air

resistance is not neglected. Figure 1 shows these forces acting on a

falling object. The object shown is a coffee filter. Its light weight

and wide cross-sectional area makes this an ideal candidate for this

experiment.

Gravitational force ( ) remains constant as the filter

falls. The force due to air resistance, however, increases as the speed

of the filter increases. Air resistance is then proportional to velocity.

A general equation for air resistance (or drag force) can be written

as

(1)

where is a constant (which includes aerodynamic properties of the

filter) and is the exponent of velocity.

Eventually, the drag force will have the same magnitude of the gravitational force. At this point,

the net force will be zero and both forces can be equated to one another

(2)

According to Newton’s second law ( ), if the net force is zero, then the acceleration is zero as well, keeping the coffee filter dropping at a constant velocity. This velocity is called

terminal velocity. You will measure and use this terminal velocity to found from equation (2).

Procedure:

This experiment will once again utilize Tracker to plot the distance of the falling object

as a function of time. Therefore, you will need to record videos of the coffee filters falling and

analyze those videos on Tracker.

1. With a video camera or other device, record video of the coffee filters being dropped

from a height of about 2 meters. You will start by dropping all the coffee filters at once.

IMPORTANT: Do not pull the coffee filters apart from one another. Keep the filters

compact as given in class. The mass of the coffee filters were measured in class to

ensure that you are starting with the number written on the filters. Each coffee filter is

0.86 g (see the datasheet).

Air Resistance

velocity

Fg

Figure 1

You will need to make sure that the requirements for the video are being met as last time.

These requirements are:

 Avoid white backgrounds. It will be easier to track the filters if the walls are

darker. Some suggestions are wooden doors, painted walls, or brick walls.

 The complete motion must be captured on the video. This includes the point

of release and the point of contact to the ground.

 Your video should be leveled with the ground. The camera should not be tilted

downwards but straight. Position your camera at the midpoint of the final and

initial position of the filter. This will minimize the tilt of the camera.

 There must be an object of known length on the video at all times. Placing or

taping a ruler or a meter stick on the wall where the coffee filters are dropped

is suggested.

2. Download the video files to a computer and open the Tracker software. You will do a

very similar analysis to the free-fall lab. Review the video tutorial if needed.

3. Open the video file in the Tracker software. Be sure to rotate the video (if needed), add

the calibration stick, set up coordinate axes, and select a point mass on the filter. You

may review the video tutorial “calibration.mp4” which can walk you through this step. A

link to the video is found on Moodle.

4. Adjust the playback of the video to the moment the coffee filters are released. Place the

black triangle at this position.

5. You are now ready to track the coffee filters. Select the coffee filter in each frame by

pressing the shift button while clicking on the coffee filter. See the video tutorial

“calibration.mp4”.

6. Click on the y-axes label “x” on the graph located on the right-hand side. Change the

vertical axes to “y: position y-component”.

7. Now you can analyze the data. Go the menu bar and click Views>>Data tools (Analyze..)

A graph should pop up with the vertical axis labeled “y” and the horizontal axis labeled

“t”.