Indiana University – Purdue University Fort Wayne
Opus: Research & Creativity at IPFW
Physics Faculty Presentations
Department of Physics
Winter 1-10-2011
Helping Students Understand the Work-kinetic
Energy Theorem
Brian Baumann
Indiana University - Purdue University Fort Wayne, [email protected]
Mark F. Masters
Indiana University - Purdue University Fort Wayne, [email protected]
Jacob Millspaw
Indiana University - Purdue University Fort Wayne, [email protected]
Eric Ayars
California State University - Chico, [email protected]
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Part of the Physics Commons
Opus Citation
Brian Baumann, Mark F. Masters, Jacob Millspaw, and Eric Ayars (2011). Helping Students Understand the Work-kinetic Energy Theorem.
Presented at American Association of Physics Teachers Winter Meeting, Jacksonville, FL.
http://opus.ipfw.edu/physics_facpres/44
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Helping Students Understand the Work-kinetic Energy Theorem
Brian Bauman, Mark F. Masters, Jacob Millspaw
Department of Physics, Indiana University Purdue University Fort Wayne
Eric Ayars
California State University, Chico
Pushing away – No Change in Direction
Below is sample data with the fan oriented to increase
the speed of the cart in its initial direction of travel.
Fan Off
0.12
Fan On
0.1
Fan Off
0.08
ⵠ(V )
0.47
0.45
0.43
0.41
0.39
0.37
0.35
0.33
2
2.5
3
3.5 4 4.5
Time (s)
5
5.5
6
Using the separation distance between the magnets and
the initial and final velocities we can calculate the force
of the fan using the Work-Energy theorem.
1
1
2
2
Work = F net⋅d = KE= mv f − mv i
2
2
Magnetism to the Rescue
We use a fan cart with a reed switch (shown above) and a
micro controller (Thanks Eric) to turn the motor on and off
at various preset positions on the track with magnets.
With this, we can now explore the relationship between
the force exerted, the distance traveled and the speed of
the cart (after the fan has been turned off).
The resulting force can be easily compared to the force
determined using the slope of the velocity vs time graph
(where the fan is on) and Newton's 2nd Law.
F net =ma
Both forces are in agreement as expected!
Pushing Back – Force opposing initial velocity
The data below was taken with the fan oriented in the
opposite direction. The cart launched out and slowed.
Fan Cart
Spring Launcher
Velocity vs. Time 9
Power On
Magnet
Magnetic Switch
Power Off
Magnet
Below is a typical configuration for such an experiment.
The fan cart is set in motion with a spring launcher and
then a constant force is applied by the fan over the
distance between the two magnets.
Velocity (m/s)
0.6
Fan Off
Fan On
0.5
0.4
Results
Below is a plot showing the relation between the change
in the square of the velocity and the displacement that
the fan force acted over (all taken with the fan force
directed in the direction of the initial velocity).
2
Velocity (m/s)
Trouble with Fan Carts?
There are seemingly limitless general physics labs that
probe concepts related to motion and forces, many of
which use a standard fan cart. When it comes to
examining the relationship between work and kinetic
energy the number of investigations is a bit more limited.
The fan cart (while found in almost every intro physics lab)
has a major limitation; it is always on or always off!
Slope here due
to friction
Fan Off
0.3
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (s)
Here we can see that the acceleration of the fan cart is
some variable (as the fan powers up).
0.06
0.04
f(x) = 0.19x - 0.01
0.02
0
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Distance (m)
The data points can be fit to a line representing a
constant force close to that calculated using Newton's
nd
2 law. The slope represents the net force on the fan
cart.
Troubles
There are some kinks that need to be worked out. The
reed switch is not the best option as it periodically
failed to activate or deactivate the fan. The spin up
time of the motor is also a factor because the higher
the velocity of the fan, the longer spin up time of the
motor.
Conclusion
All in all the position switchable fan cart shows promise
for use in constant and variable force related work and
energy investigations. It allows for investigations that
were previously unavailable with the always on or
always off fan carts.
More complex versions that can be configured to change
speed or fan directions during runs are a fun and hopeful
future for the switchable fan cart helping students to
develop a more complete understanding of the WorkEnergy theorem!