Purpose: To study the relationship between air drag forces and the velocity of a falling
body.
Equipment: Computer with Logger Pro software, lab pro, motion detector, nine coffee filters,
meter stick.
Introduction: When an object moves through a fluid, such as air, it experiences a drag force that
opposes its motion. This force generally increases with velocity of the object. In
this lab we are going to investigate the velocity dependence of the drag force. We
will start by assuming the drag force, FD, has a simple power law dependence on
the speed given by:
1) F(drag) = k|v|^n, where the power n is to be determined by the experiment.
This lab will investigate drag forces acting on a falling coffee filter. Because of the
large surface area and low mass of these filters, they reach terminal speed soon after
being released.
Procedure:
Note: You will be given a packet of nine nested coffee filters. It is important that the shape of this packet stays the same throughout the experiment so do not take the filters apart or otherwise alter the shape of the packet. Why is it important for the shape to stay the same? Explain and use a diagram.
Note: You will be given a packet of nine nested coffee filters. It is important that the shape of this packet stays the same throughout the experiment so do not take the filters apart or otherwise alter the shape of the packet. Why is it important for the shape to stay the same? Explain and use a diagram.
- Shape is important because the amount of drag produced depends on the surface area of the object. This way once the filters are released they accelerate until they reach terminal velocity.
1. Login to your computer with username and password. Start the Logger Pro software, open the
Mechanics folder and the graphlab file. Don’t forget to label the axes of the graph and create an appropriate title for the graph. Set the data collection rate to 30 Hz.
2. Place the motion detector on the floor facing upward and hold the packet of nine filters at a minimum height of 1.5 m directly above the motion detector. (Be aware other of nearby objects which can cause reflections.) Start the computer collecting data, and then release the packet. What should the position vs time graph look like? Explain.
- Our position vs time graph should show our object is decreasing in position while gaining speed in the negative direction. Then it becomes linear to show it has reached terminal velocity, we know this since our slope would be constant, thus the linear graph.
Verify that the data are consistent. If not, repeat the trial. Examine the graph and using the mouse, select (click and drag) a small range of data points near the end of the motion where the packet moved with constant speed. Exclude any early or late points where the motion is not uniform.
3. Use the curve fitting option from the analysis menu to fit a linear curve (y = mx + b) to the selected data. Record the slope (m) of the curve from this fit. What should this slope represent? Explain.
- Our slope represents our terminal velocity since it's showing that our object is moving with a constant speed
Repeat this measurement at least four more times, and calculate the average velocity. Record all data in an excel data table.
4. Carefully remove one filter from the packet and repeat the procedure in parts 2 and 3 for the remaining packet of eight filters. Keep removing filters one at a time and repeating the above steps until you finish with a single coffee filter. Print a copy of one of your best x vs t graphs that show the motion and the linear curve fit to the data for everyone in your group (Do not include the data table; graph only please).
5. In Graphical Analysis, create a two column data table with packet weight (number of filters) in one column and average terminal speed (|v|) in the other. Make a plot of packet weight (y-axis) vs. terminal speed not velocity (x-axis). Choose appropriate labels and scales for the axes of your graph. Be sure to remove the “connecting lines” from the plot. Perform a power law fit of the data and record the power, n, given by the computer. Obtain a printout of your graph for each member of your group. (Check the % error between your experimentally determined n and the theoretical value before you make a printout – you may need to repeat trials if the error is too large.)
% diff = |2 - 2.14 / 2 | x 100
= 7 % diff
6. Since the drag force is equal to the packet weight, we have found the dependence of drag force on speed. Write equation 1 above with the value of n obtained from your experiment. Put a box around this equation.
Look in the section on drag forces in your text and write down the equation given there for the drag force on an object moving through a fluid. How does your value of n compare with the value given in the text? What does the other fit parameter represent? Explain.
Drag = 1.90v^2.14
Look in the section on drag forces in your text and write down the equation given there for the drag force on an object moving through a fluid. How does your value of n compare with the value given in the text? What does the other fit parameter represent? Explain.
D= (1/4)A*v^2
We recorded our n to equal 2.14 which is close to the value that was given in the text of n=2. The other fit parameter represents the objects shape and and the density of the conditions which is moving through. The cross-section of our object is represented by A.
Conclusion: In this lab we got a 7 % difference which shows that we weren't too far of from our accepted value. A cause for error could be that our coffee filters weren't neatly stacked so our drag force was not uniform. Another source of error came from using terminal speeds that were not consistent with out other trials, since our coffee filters wouldn't always land close to our motion detector.We also rounded our numbers so our calculations might not have been as accurate as we might have wanted them to be.
