Unformatted text preview: Kristina Kuil
Rebecca Merrill Liz Kunkler
PHY 151L / Report No. 07
Air Resistance Objectives:
➢ Observe the effect of air resistance on falling coffee filters, forming data plots for both position
and velocity versus time for a filter released from rest in air.
➢ Determine how air resistance and mass affect the terminal velocity of a falling object.
➢ Choose between two competing force models for the air resistance on falling coffee filters.
➢ Form free-body diagrams for each phase of motion experienced by the coffee filter from its
release, to the point where it reaches terminal velocity, to its impact with the ground.
● Vernier computer interface
Logger Pro and Microsoft Excel
Vernier Motion Detector
5 basket-style coffee filters Diagram of Setup: Preliminary Questions:
1. Hold a single coffee filter in your hand. Release it and watch it fall to the ground. Next, nest
two filters and release them. Did two filters fall faster, slower, or at the same rate as one
filter? What kind of mathematical relationship do you predict will exist between the
velocity of fall and the number of filters?
➢ Two filters fell faster than one filter when released from your hand. The mathematical
relationship that exists is, the more filters that are dropped, the faster the velocity will
2. Sketch your prediction of a graph of the velocity vs. time for one falling coffee filter. 3. If a filter is moving at a constant velocity, what do you know about the forces on the filter?
Be specific, and describe what logic leads you to form your conclusion.
➢ If a filter is moving at a constant velocity, the net force acting on it is zero. This is
because the, if velocity is constant, that means that acceleration is equal to zero. In the
equation F = ma , if acceleration is equal to zero, then the net force is also equal to zero.
Data & Observations:
Number of Filters Terminal Velocity
VT (m/s) 1 -0.9974 0.9948 2 -1.409 1.985 3 -1.513 2.289 4 -1.781 3.172 5 -2.579 6.551 Noteworthy Observations: (Terminal Velocity)
VT 2 (m 2 /s 2 ) 2 ➢ The terminal velocity of the coffee filter increases as the number of filters (mass)
Results of Analysis: Questions:
1. Use a drawing program to draw a free body diagram of a single falling coffee filter during
each of the following phases: Before release, immediately after release, a “short” time after
release, a “long” time after release, just as it makes impact with the ground, and after it
makes impact with the ground.
No exact values are needed, but it is important to clearly label the forces acting on your
coffee filter and represent the air drag force with respect to the weight vector of your filter.
Additionally, note the value for the net acceleration of the filter at each phase relative to
the acceleration due to gravity. (i.e. a = g, a < g, a= 0, etc.) ➢
2. Provide a general expression for the acceleration a of an object experiencing air drag in
terms of mass m, acceleration due to gravity g, and air drag Fg.
➢ a= mg−F
m g 3. What specific characteristics from both your position vs. time and velocity vs. time plots
allowed you to conclude the filter had reached terminal velocity? Support your response
with clear reasoning.
➢ We determined that the filter reached terminal velocity when the position vs. time slope
had a constant slope, and velocity vs. time had a slope of zero. In the position vs. time
plot, the velocity was terminal at a constant slope, this constant slope represents
constant velocity. When an object has constant velocity, the acceleration is equal to zero.
For the velocity vs. time plot, the slope was zero. Because the slope of this plot
represents the acceleration, this shows that the acceleration of the filter was zero,
meaning that it was at terminal velocity.
4. Depending on the object, the drag force is either proportional to the speed of the object, or
the square of the speed of the object. From the experiment, and your Excel analysis,
considering the number of filters dropped serves as an indication for what the drag force is
(i.e. more filters, more mass; more mass, more force due to gravity; more force due to
gravity, the higher the upward drag force is when the object reaches equilibrium, as
acceleration is now zero) would you say that the drag force of an object is linearly
proportional to the terminal speed of an object in free-fall (–bv), or the terminal speed
squared (–cv2 )? Support your response with reasoning.
➢ The drag force of an object is linearly proportional to the terminal speed squared ( − cv 2
). If a graph is proportional its best fit line goes through the origin. If you look at our
graphs above, the best fit line of the terminal speed is linear but does not go through the
origin therefore it is not proportional.
5. Let's say you increase the mass of an object to twice its original value (which again,
doubles the weight, which doubles the drag force when equilibrium is reached); would you
say the terminal speed of the object (the speed at which it is no longer accelerating) also
doubles? In other words, if you drop an object that weighs 100 N and it reaches terminal
speed at 40 m/s, would a 200 N object of the same shape and size reach terminal speed at
80 m/s? Explain your reasoning by stating why you agree with that statement or not.
➢ If you were to double the weight, the terminal velocity would not double. If you look at
our graphs, the plotted points for the terminal velocity vs the number of coffee filters
increases but does not double. Something with a larger mass does fall more quickly with
air resistance than something with less mass. This was shown in the bowling ball and
feathers video. It was also shown in our graphs that the more when the number of coffee
filters was doubled, the terminal velocity increased but did not double. Kristina and
Andrea also tried this on our own but dropping one plastic cup and four plastics cups,
and the four plastic cups fell more quickly, but not twice as fast. 6. Consider the relationship you determined between the number of coffee filters dropped and
the terminal speed of those filters; by now, you’ve either concluded that the number of
filters dropped relates linearly to the terminal speed of the filters, or the terminal speed
squared. Using your conclusion as a guide, how does the time of fall relate to the weight of
the coffee filters? If one filter falls in time “t ”, how long (in terms of “t”) would it take four
filters to fall, assuming they reached terminal speed very quickly?
➢ The number of coffee filters related linearly to the terminal speed. As the weight of the
coffee filters increases, the time it takes for them to fall decreases. If one filter falls in
time “t,” then it would take four filters to fall in about “⅓ t” because even though the it
relates linearly it does not relate proportionally. The more mass added the shorter the
time it takes to fall, however each coffee filter added does not cut the time in half when
7. Suppose you were to analyze the motion of a college physics textbook dropped in a similar
manner to that which you released your coffee filters; how would you expect the position vs.
time and velocity vs. time plots for this object to compare to those for your coffee filters? Be
sure to clearly state any expected similarities and differences.
➢ The slope of the dropped book is steeper than that of our coffee filters. A difference in
the plots is that the velocity does not become constant at any point for the book
dropping as it did for the coffee filters. This is because the book is so heavy that air
resistance never equals the gravitational force on the book in the short distance it is
dropped. A similarity is that, as we increase the number of coffee filters, the slopes get
steeper due to the increasing weight of the coffee filters. This is similar to the book
because the book is heavy and its slope is steep due to this. ...
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