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AP Physics C Unit 1 Lab:

Drag Force on a Coffee Filter

Purpose: To study the relationship between air drag forces and the velocity of a falling body.

Equipment: Stopwatch, coffee filters (at least 5-7), meter stick or measuring tape, Desmos.com or other graphing website/application.

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 the relative velocity between the fluid and the object. The drag force also depends on other quantities such as the size, shape, and mass of the object, as well as the density and viscosity of the fluid. In this lab we are only going to investigate the velocity dependence of the drag force. We will start by assuming the drag force, F_D, has a simple power law dependence on the speed given by:

F_D = k |v|ⁿ,

where the power n is to be determined by the experiment.

When an object is released from rest, it initially experiences no drag force. As it falls its speed increases and so does the drag force acting on it. Eventually, the drag force is as large as the force of gravity and then the net force acting on the object is zero. At that point, the speed becomes constant. We call this final speed the terminal speed for the object. This lab will investigate drag forces acting on falling coffee filters. Because of the large surface area and low density of these filters, they reach terminal speed soon after being released.

Procedure: You will need to brainstorm and write a short procedure that allows you to determine the terminal velocity of the coffee filters and plot vs. the weight of the filters.  Here are some hints:

NOTE: 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.

Hints:

1.     Choose a starting height to drop your coffee filters from.  This height should be at least 1m above the ground

2. Drop the # of coffee filters indicated in the table and measure your values at least 3 times

3. Repeat steps 1-2 for the remaining trials, varying the # of filters. Keep adding filters one at a time and repeating the above steps until you finish with eight filters.

4. Measure and record the mass of each set of filters and then calculate their weight.  You may need to do a quick google search for the average mass of your particular coffee filter.

5. We can’t measure terminal velocity easily without a motion detector, but you can estimate it by realizing that the filters reach terminal speed soon after being released, which therefore means that Terminal Velocity ~ Average Velocity.

6. Open up the graphing program of your choice and plot the drag force (F_d) vs. the terminal velocity.  Hint: how does the drag force compare to the force of gravity when terminal velocity is reached?

7. Find a fit for your data, either by linearizing, or trying different fits until you determine the relationship between your variables.

On your lab writeup, draw and label a free body diagram for the following conditions: Use the SIZE of arrows top indicate whether a certain force is larger or not.

a) An object falling in a vacuum

b) An object falling in air the instant after is was released

c) An object falling in air a long time after release

Postlab Questions (answer at end of lab report):

1. Write the complete drag force equation from your graph.

2. The filters do not reach terminal velocity instantly.  What effect does this have on your data?  

3. From your data or graph, estimate a value for “k” and state the numerical value and its units.

4. From your data, you should be able to guess whether the air friction is linear (proportional to v¹), quadratic (proportional to v²), or proportional to a higher power of n (vⁿ) when n > 2.  Which seems to fit your data best?  Look at the section in your textbook on air friction and write a few sentences on how your data fits in with “low-speed” or “high-speed” air resistance.