Re: friction frustration

["John S. Denker" <jsd@MONMOUTH.COM>]

Matt Harding wrote:

> ... carts on an inclined ramp....
> 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.

Close enough.

> 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 ... in
> order to have a more accurate prediction for acceleration.

So why didn't you take the fourth data point?????

Data is data.  Data is sacred.  Don't let your preconceived
notions prevent you from going where the data leads you.

> I'm assuming the main source of friction that we're dealing with is
> occurring where the axle meets the bearings

Yes, that's probably dominant.

> 1.   Should that amount of friction not be decreasing with an
> increase in angle for the ramp?

Well, OTBE (Other Things Being Equal) it should be slightly
decreasing.  In the limiting case of a 90 degree incline,
the wheels should produce no friction at all.

However, in the other limit, namely small angles, the
decrease in weight on the wheels is small squared.  What do
you think the cosine of 10 degrees is?

Meanwhile, assuming OTBE is a bad assumption.  While the
load on the wheels is decreasing in second order, other
contributions are increasing to first order.  For starters,
I suspect the wheel-bearing friction depends on _speed_ as
well as load ... and at the steeper angles the card is just
plain going faster.  Indeed it's hard to imagine a physical
process that would produce friction independent of speed.

> The ramps were only 1m long, and 0.5 m of that is
> useable because of the detectors personal buffer space.

A longer ramp would allow you to control for velocity-dependence.
Ramp-making materials are available at the local home center.

This posting is the position of the writer, not that of the Skipper, the
Howells, Ginger, or Mary Ann.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.