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I teach several sections of high school physics, and ran in to the sa=
me
problem consistently during a recent activity. I was doing a lab wit=
h
carts on an inclined ramp. The intent was to have the students predi=
ct
the acceleration for the cart based on the angle of the incline and t=
he
weight of the cart. They were to then find the actual value for
acceleration using Mac Motion with sonic ranger motion detectors. =
=20
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 forc=
e
resulting in less friction). However, when I tried to have them wor=
k
backwards from the actual acceleration to eventually arrive at a valu=
e
for friction, they consistently found that the amount of friction was
increasing as the angle increased.
Here's how the calculation worked.
Cart mass =3D 1.26 kg
Incline =3D 3.1 degrees
x-component of force =3D 0.67 N
ideal acceleration =3D 0.53 m/s/s
=20
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 tha=
t
amount of acceleration,=20
1.26kg*0.27m/s/s =3D 0.34 N
=20
I assumed that the difference between the forces ( 0.67 - 0.34 =3D 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=3D10.56 degrees
x-component of force =3D 2.26N
ideal acceleration =3D 1.79 m/s/s
=20
=2E..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 =
=3D
0.54 N). So it would appear that increasing the angle resulted in mor=
e
friction. OOOPS!
=20
My goal was to have an extension to the lab where they would work wit=
h a
fourth angle, but calculate the amount of friction beforehand based o=
n
coefficient of friction and normal force (I had hoped to return
consistent values for the coefficient of friction for the three initi=
al
angles, but the coefficient of friction was apparently increasing) in
order to have a more accurate prediction for acceleration.
=20
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). =20
1.=09Should that amount of friction not be decreasing with an
increase in angle for the ramp? =20
=20
=20
2.=09Am I fundamentally flawed in my assumptions for friction in this
lab?
=20
=20
I'm fairly confident in the mac-motion values, the acceleration graph=
s
ended up having obvious horizontal regions, and the students were abl=
e
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.
=20
Help?
=20
Thanks,
Matt Harding
Iowa City West High School
=20
=20
=20
=20
This posting is the position of the writer, not that of SUNY-BSC, NAU or
the AAPT.