To use the LabPro, Motion detectors, and a laptop computer to produce position vs. time and velocity vs. time graphs and to analyze them to determine how mass and surface area affects the terminal velocity of a falling object.
Galileo attempted to prove that objects in free fall accelerate downward at the same rate. This means that no matter what the mass or size of an object is it will still fall at the same acceleration. This free fall acceleration value is -9.81 m/s 2 .
Galileo’s theory only works in a vacuum, however. In the real world many other factors have an influence on the acceleration of a falling object. A major factor is air resistance. The force of air resistance actually pushes upward on a falling object, thus decreasing the acceleration. The amount of air resistance on an object is affected by properties of the object, one of which is surface area.
While air resistance causes objects to accelerate differently from Galileo’s theory, it is not necessarily a bad thing. In fact, if it weren’t for air resistance many inventions would not work. For example, a large, wide parachute is able to slow a falling object’s acceleration because of air resistance. Parachutes tend to have a large surface area so that the object will slow down enough to land safely on the ground.
Air resistance causes objects to reach a maximum velocity called terminal velocity. The terminal velocity is affected by factors that influence air resistance such as shape, mass, and surface area. It is possible to use motion detectors to produce graphs of an object’s position, velocity, and acceleration, which can then be analyzed to determine how these factors change an object’s acceleration and terminal velocity.
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Computer

Right-angle clamp
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Vernier LabPro

Basket coffee filter
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Vernier Motion Detector

Book

Logger Pro

Meter stick

Masking tape

Metal rod
Setup
See figure 1.
Lab Pro
Figure 1
Motion detector

Using a computer and a motion detector, drop a book and a coffee filter under the motion detector and record the data in separate runs on the computer. Use the computer to determine the maximum velocity of the book and the coffee filter. Clear the data, fold the coffee filter in half, and drop the coffee filter under the motion detector again. Continue to fold the coffee filter and drop it under the motion detector until it has been folded three times. Use the computer to find the terminal velocities of each of the coffee filters with a different number of folds. Stack two coffee filters on each other and drop them under the motion detector. Continue add two more coffee filters and drop them under the motion detector until it 10 coffee filters are stacked on each other. Use the computer to find the terminal velocities of each of the stacks of coffee filters.
Part A
Coffee Filter Book
Maximum Velocity = 0.989 m/s Maximum Velocity = 4.274 m/s
Part B
# of Folds
0
1
2
3
Terminal Velocity
0.5619 m/s
0.7458 m/s
1.982 m/s
0.9943 m/s
Part C
# of Coffee Filters
2
4
6
8
10
Terminal Velocity
0.9525 m/s
1.394 m/s
1.600 m/s
1.777 m/s
1.971 m/s

There were no calculations for this lab.
Part A
Part B – Whole Filters

Part C
– 4 Filters

While there is not a large amount of mathematical error in this lab, error still exists in other forms. One source of error would be the coffee filter falling out of the range of the motion detector as it fell. This would cause the graphs to appear as if the coffee filter had hit the ground when it was actually still fall out of the range of the motion detector. Another source of error would be interference from our hands and arms. While we did our best to throw out data that included the motion of our hands, there may be smal l in the graph that we didn’t notice.
Questions
1. The graph of the book has a slope that is much greater and more positive than the coffee filter because the book has a greater mass. Since the mass is greater, it will have a greater free fall acceleration and a greater terminal velocity. This means the coffee filter fell much more gradually than the book because it has a smaller mass.
2. The book’s velocity graph is tall, steep, and lasts over a small period of time. On the contrar y, the coffee filter’s velocity graph is short and lasts over a long period of time. This is due to the fact that the book has a greater mass than the coffee filter. Therefore the book had a greater increase in velocity in a shorter period of time, which caused it to hit the ground first. The coffee filter did not experience as great of a jump in velocity and took much longer to fall because of its mass.
3. Yes, the book reached terminal velocity. I know this because the velocity graph of the book shows that it peaked and flat lined at the top of the spike. Since terminal velocity is the maximum velocity, this peak is the terminal velocity of the book. After it reached terminal velocity it hit the ground and produced the steep downward slope.
4. As the surface area of the coffee filter was reduced by increasing the number of folds, the terminal velocity increased. This is because the air resistance does not have as much to resist when the surface area decreases. Since air resistance is the force that opposes gravity and causes the object to slow down, a decrease in air resistance would allow the object to reach a greater maximum, or terminal, velocity. The more you decrease the surface area while keeping the force of gravity the same, the greater the terminal velocity will be.
5. As the mass of the coffee filters was increased by adding more coffee filters the terminal velocity increased. This is because there will be a greater force of gravity pulling down on the coffee filters. This greater force of gravity will outweigh the force of air resistance since the surface area remained the same and therefore the coffee filters will be able to reach a greater terminal velocity.

c. b.
The more you increase the force of gravity while keeping the force of air resistance the same, the greater the terminal velocity will be.
6. a.
F
F
G
Air Resistance
F
F net net
= F
= F
G
G
– F
Air Resistance
F
F
G
Air Resistance
F
G
= F
Air Resistance
F
G
7. The acceleration graph will show the acceleration increasing at first. This is becau se the only force acting upon the object is the force of gravity and Newton’s second law states that the acceleration is directly proportional to the net force acting upon the object. Then as air resistance starts to become a force the acceleration will start to turn in the other direction and decrease. Once again this is because of Newton’s second law and the fact that acceleration is directly proportional to the net force. This time the net force is gravity minus air resistance, so since the net force is less the acceleration will become less as well. Finally the graph will show the object reaching terminal velocity when the acceleration is at zero. The net force is zero because the force of gravity equals the force of air resistance, so according to Newton’s second law the acceleration would be zero as well (a=f/m=0/m=0).

Conclusion
In this lab we were able to learn how mass and surface area affects the terminal velocity of an object. This lab was very interesting to me because I was able to predict and reason out the effects on the terminal velocity and then see them prove to be correct. I now have a better understand of why mass and surface area changes the terminal velocity and I am able to analyze the graphs better. I think our experiment was successful because the graphs showed the correct trends for the most part. The trial with two folds was skewed, but we were able to recognize this and ignore it when determining the trends in the terminal velocities. If I were to perform this experiment again I would figure out a better way to drop the objects so that there was less interference in the data due to the movement of arms and hands. We had to redo our trials several times because of this, so it would be nice to find a way to fix this problem.
Overall I enjoyed this lab and I learned a lot about terminal velocity and the variables that affect it.