What is the drag coefficient of a coffee filter

Physics Lab Experiment

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”.

8. Click on the Analyze button on the top of the graph and select “Statistics” as well as

“curve fit”. You will see a linear fit to your data as soon as your select “Curve fit”.

9. Observe the data points of the graph. It should be parabolic at first and eventually

become linear. The linear part of the graph is when the terminal velocity has been

reached. Select the points that appear to be the most linear by left-clicking on the graph

and dragging the mouse over the points you want to select (see “data.mp4”). Tracker will

fit this to a straight line of the form x=A*t+B. The physical interpretation of the slope, A,

is the terminal velocity. Record the value for A and the correlation coefficient (see

“calibration.mp4” if needed) on your data sheet. Be sure to include units.

10. Remove only one coffee filter at a time from the stack. It is important that the other

coffee filters are not separated in order to keep them compact.

11. Repeat steps 1- 11 until you have no more coffee filters to remove. By the end of the

experiment, you should have five values of terminal velocity.

Analysis:

1. Multiply the number of coffee filters to to calculate the gravitational force on

the filters. Since you are calculating force, your units of the mass must be in kilograms.

You should be obtaining values of 0.0088 N, 0.0176 N, etc.

2. Now that the data has been obtained, you will determine the value of the from equation(2). This can be done with Microsoft Excel. Enter the gravitational force and the

terminal velocity in two adjacent columns, as shown below. Be careful with your units.

3. Highlight the numbers in the columns. Click on Insert tab located near the top of the

screen. In the chart sections, select the scatter plot (the graph that only has data points and

no lines). You should see a graph similar to the one below. Notice that the velocity values

are on the x axis and the weight are on the y axis.

4. You can add labels on your axes by selecting the graph and going to the layout tab at the

top of the program. Enter labels under “Axis Titles.”

5. To fit a curve to the data points, right click on the data points and select “Add

Trendline…” A dialog box similar to the one shown below should appear.

6. Select the power option, as shown above. Check the box next to “Display Equation on

chart” and “Display R-squared value on chart”. Press close. You should now see an

equation on the chart with the correlation coefficient.

7. You finally have the value for from equation (2). Record this value on your data sheet.

8. Complete your analysis by answering the questions on the data sheet. As in the last

experiment, you will need to show a screenshot from the Tracker program of each group

member dropping a coffee filters. In addition to this, a screenshot of at least on fitted

graph from Tracker per group member is required. Finally, the graph from excel with the

equation displayed must be included in your lab report.

Each group must turn in one data sheet for the whole group with calculations and the questions.

This will be turned in along with the screenshots. However, each member of the group must

write a response to the questions provided on the data sheet in his/her lab notebook. You must

still detail the experiment itself in the lab notebook, as explained in class and in the lab manual

(see page v in lab manual).