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 still start by assuming the drag force, Fd, has a simple power law dependence on the speed given by Fd= 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.
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.
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.
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.)
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.
Our data:
The slope of
Time vs. Position graph represents the terminal velocity (positive direction is upward). So on this graph, the terminal velocity is -1.66m/s. The terminal speed is 1.66m/s.
On this graph, the terminal velocity is -1.99m/s. The terminal speed is 1.99m/s.
Our data:
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| Time vs. Position graph when there is 5 filters |
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| Time vs. Position graph when there is 8 filters |
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| The average terminal speed of 1-9 trails |
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| The number of filter vs. average speed graph |
Question:
(1)Why is it important for the shape to stay the same?
---Because the drag relates to objects' cross section area. If filter's shape changes, then it's drag will also change.
(1)Why is it important for the shape to stay the same?
---Because the drag relates to objects' cross section area. If filter's shape changes, then it's drag will also change.
(2)What should the position vs time graph look like?
---The curve decreases faster and faster at first. Then, at a moment, the curve turns to be linear, decreases with constant slope.
(3) What should this slope represent (y = mx + b)?
---The slope m represents the terminal velocity.
(4)How does your value of n compare with the value given in the text? What does the other fit parameter represent?
---We find n is 1.95, which is almost 2. That means it matches to the value that given in the text that n=2.
Because Mg= (1/4)Av^2 (A= cross section area). We found that Y=2.14X^1.95 (X= terminal speed; Y= number of coffee filters). So. Y× mg= (1/4)A×(X^2) (m= mass of each coffee filter). Also, Y= [A/ (4gm)]× (X^2). So 2.14 represents A/ (4gm): the cross section area of coffee filter divides four times a coffee filter's gravity force.
---The curve decreases faster and faster at first. Then, at a moment, the curve turns to be linear, decreases with constant slope.
(3) What should this slope represent (y = mx + b)?
---The slope m represents the terminal velocity.
(4)How does your value of n compare with the value given in the text? What does the other fit parameter represent?
---We find n is 1.95, which is almost 2. That means it matches to the value that given in the text that n=2.
Because Mg= (1/4)Av^2 (A= cross section area). We found that Y=2.14X^1.95 (X= terminal speed; Y= number of coffee filters). So. Y× mg= (1/4)A×(X^2) (m= mass of each coffee filter). Also, Y= [A/ (4gm)]× (X^2). So 2.14 represents A/ (4gm): the cross section area of coffee filter divides four times a coffee filter's gravity force.
Conclusion:
In this lab, we study the relationship between air drag forces and the velocity of a falling body. According to our graph and data, we notice that when an object begins to fall, its speed gradually increases at first. Then, at a moment, the velocity will be constant, and this object will maintain this condition until it toughs down. The reason is that when the speed is increasing, the Drag is also increasing, that Drag= k |v| ^2. The net force of object is Mg-Drag, so acceleration= (Mg-Drag)/M. The Drag is increasing, the acceleration is decreasing. When Drag is equal to mass of the object, the acceleration turns to be zero. So the object will keep falling will constant velocity.
The causes of error:(1) When filters are falling, their shapes are easy to change. Because drag relates to objects' cross section area, so if filters' shapes change, the drag will also change.
(2) The filters in the air may be influenced by wind, so they may have extra horizontal velocities. So, the velocity we got may be not correct.
(3) We use rounding values to get the "number of filter vs. average speed graph", so it can't be exactly correct.
nice work -- grade == s
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