I teach several sections of high school physics, and ran in to the same
problem consistently during a recent activity. I was doing a lab with
carts on an inclined ramp. The intent was to have the students predict
the acceleration for the cart based on the angle of the incline and the
weight of the cart. They were to then find the actual value for
acceleration using Mac Motion with sonic ranger motion detectors.
I was hoping that as the students increased the angle of the ramp,
they would have better agreement between predicted and actual values for
acceleration due to the decrease in friction (decrease in normal force
resulting in less friction). However, when I tried to have them work
backwards from the actual acceleration to eventually arrive at a value
for friction, they consistently found that the amount of friction was
increasing as the angle increased.
Here's how the calculation worked.
Cart mass = 1.26 kg
Incline = 3.1 degrees
x-component of force = 0.67 N
ideal acceleration = 0.53 m/s/s
Analyzing the acceleration graph in mac motion gave an average
acceleration of 0.27 m/s/s
Then I had them work backwards to find the force that would cause that
amount of acceleration,
1.26kg*0.27m/s/s = 0.34 N
I assumed that the difference between the forces ( 0.67 - 0.34 = 0.33N )
would more or less be attributable to friction.
However, when I had them increase the angle (using same cart and ramp)
they got numbers like this...
Incline=10.56 degrees
x-component of force = 2.26N
ideal acceleration = 1.79 m/s/s
...and mac motion returned an average acceleration of 1.37 m/s/s,
meaning the force was 1.72 N. The difference would be (2.26 - 1.72 =
0.54 N). So it would appear that increasing the angle resulted in more
friction. OOOPS!
My goal was to have an extension to the lab where they would work with a
fourth angle, but calculate the amount of friction beforehand based on
coefficient of friction and normal force (I had hoped to return
consistent values for the coefficient of friction for the three initial
angles, but the coefficient of friction was apparently increasing) in
order to have a more accurate prediction for acceleration.
I'm assuming the main source of friction that we're dealing with is
occurring where the axle meets the bearings (we're using some older
wooden carts with less-than-"frictionless" bearings).
1. Should that amount of friction not be decreasing with an
increase in angle for the ramp?
2. Am I fundamentally flawed in my assumptions for friction in this
lab?
I'm fairly confident in the mac-motion values, the acceleration graphs
ended up having obvious horizontal regions, and the students were able
to analyze those sections to get a solid average value. The only
problem I can see with the data collection comes from the small data
collection period. The ramps were only 1m long, and 0.5 m of that is
useable because of the detectors personal buffer space.
Help?
Thanks,
Matt Harding
Iowa City West High School
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.