Download Terminal Velocity Lab

Terminal Velocity Lab
Gage Ames
Zack Armagost and Paul Armagost
Physics - Period 2
Monday, November 17, 2008
Purpose
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.
Background Information
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/s2. 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.
Equipment and Setup
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Computer
Right-angle clamp
Vernier LabPro
Basket coffee filter
Vernier Motion Detector
Book
Logger Pro
Meter stick
Masking tape
Metal rod
Motion detector
Lab Pro
Setup
See figure 1.
Figure 1
Procedural Summary
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.
Data
Part A
Coffee Filter
Book
Maximum Velocity = 0.989 m/s
Maximum Velocity = 4.274 m/s
Part B
# of Folds
Terminal Velocity
0
0.5619 m/s
1
0.7458 m/s
2
1.982 m/s
3
0.9943 m/s
# of Coffee Filters
Terminal Velocity
2
0.9525 m/s
4
1.394 m/s
6
1.600 m/s
8
1.777 m/s
10
1.971 m/s
Part C
Calculations
There were no calculations for this lab.
Graphs
Part A
Part B – Whole Filters
Part C – 4 Filters
Error Analysis
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 small in the graph that we didn’t notice.
Questions and Conclusions
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 contrary, 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.
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.
Fnet = FG
FG
b.
FAir Resistance
Fnet = FG – FAir Resistance
FG
c.
FAir Resistance
FG = FAir Resistance
FG
7. The acceleration graph will show the acceleration increasing at first. This is
because 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.