The total force on the Aircart includes friction. If the propeller is not
pushing the Aircart forward, friction, pushing the other direction, will
slow the Aircart down. By studying the slow-down of the Aircart as it coasts
to a stop on a level surface, you can estimate the frictional force. This
motion may be analyzed to determine the frictional force, by comparing the
work done by friction (pushing against the Aircart) and the Aircart's loss
of kinetic energy. Instead of starting from rest, the Aircart must have
an initial speed when it crosses the START line. You can use
a stopwatch to time the Aircart as it slows to a stop. If you measure
the time it takes to stop and the distance it covers before it stops, you
can calculate what you need to know.
What is your estimate of the frictional force on the Aircart? What is percent
of the propeller force is the frictional force?
Frictional Force and Speed
Investigate friction with the motor turned OFF. Otherwise things get too
complicated. The work done on the (turned off) Aircart by friction decreases
the Aircart's energy by making it slow down. How is the loss speed of the
Aircart related to its loss of energy? The Aircart looses energy when friction
does (negative) work on it. This negative work is simply the product of
the force and distance it moves. Instead of starting from rest, the Aircart
must have an initial speed when it crosses the START line. If you assume
that the frictional force is constant, then the energy the Aircart looses
will be proportional to its position (distance from start) when it stops.
You can study the relationship between friction and speed loss by examining
the two variables, stopping position and initial speed.
Measuring Average Speed with a Stopwatch
If you choose to run the Aircart on the floor, first sweep the floor. Dust
and sand are a problem.
Set up a START line for the Aircart (masking tape works well). Give the
Aircart a push (by hand) and measure both the distance it goes before it
stops, and the time elapsed between crossing the START line and stopping.
Physicists measure distance in meters, unless something more convenient
shows up. If you are working on a tile floor, the tiles are probably 1 foot
square. If so, you might want to use feet and convert to meters later (
1 foot = 0.3048 meters).
After you have set up the START line for running the Aircart, make a table
for recording the distances and times for several runs. Push the Aircart
and let it slow to a stop several times. Try different initial speeds. From
the distances and the times you can calculate average speeds.
In this problem position may be thought of as is the independent variable.
Graph initial speed vs. stopping position. Careful experimentation will
produce a graph which is not linear (not a straight line). Non-linear graphs
are a problem. Straight line graphs are nice because they lead to simple
mathematical models based on the equation for a straight line (y=mx+b).
Your data can be turned into a straight line graph by squaring one of the
variables and re plotting. From this second graph you can produce a mathematical
model relating force and initial speed. The slope of your linear graph is
proportional to the frictional force, but the Aircart mass gets into the
equation also. What is this equation?