From: Ronald Wong (ronwong@inreach.com)
Date: Tue Nov 19 2002 - 11:37:59 PST
Message-Id: <l03102802b9ffa12a9ea8@[209.209.19.235]> Date: Tue, 19 Nov 2002 11:37:59 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Center of Mass?
In response to my answer regarding a question posed by Marc Afifi, Tom asked:
>The question that's begged here is why you put the friction forces at the
>front when the back wheels are locked and at the back when the front
>wheels are locked. If wheels are locked there is still a frictional force
>acting on them so why isn't there an 'f' at both sets of wheels in both
>diagrams?
>
>Thanks,
>
>Tom Woosnam
The demonstration that Marc saw in the form of a video was a very old
demo/activity that every physics teacher is familiar with. I suspect it's
been around for at least the last couple of centuries.
There are frictional forces acting on ALL four of the cart's wheels as it
travels down the inclined plane.
As the cart travels down the inclined plane, the wheels that are locked up
(i.e. prevented from rotating) are dragged along the surface of the plane.
Because of this dragging, KINETIC frictional forces are brought to bear on
these wheels.
The remaining wheels are simply rolling down the inclined lane. This too,
can lead to frictional forces. These forces are referred to as rolling
frictional forces. They are significantly smaller than the kinetic
frictional forces (by a factor of 1/20th-1/30th when it comes to rubber and
concrete) and, on the scale of the drawing that I included with my
explanation, would amount to nothing compared to the kinetic frictional
forces. That's why they don't appear in the drawing.
Since the frictional forces oppose motion, it should have been clear which
direction the cart was traveling and therefore which end of the inclined
plane was the top and which was the bottom in the drawing.
For those of you who are not familiar with this demonstration, here is a
more complete drawing:
_________________________
Rear wheels locked up
T O P of inclined plane
f f
| ^ ^ | Direction of Motion
| | | |
| . | ||
| C M | ||
| | \/
| |
BOTTOM of inclined plane
_________________________
Front wheels locked up
T O P of inclined plane
| |
| . | Direction of Motion
| C M |
| f f | ||
| ^ ^ | ||
| | | | \/
| |
BOTTOM of inclined plane
_________________________
The forces that you see in the diagram are the kinetic frictional forces.
These forces are acting on the wheels that are locked up. The CM is in the
"center" of the cart.
The rolling frictional forces are not "pertinent" in this demo (to use Mark
Lawton's expression). They are far too small to play a major role in the
cart's behavior. So you only see the kinetic frictional forces in the
diagram.
If Marc Afifi follows my suggestion and has his students do the demo
themselves and then tells them to "play around" with it by considering
other possibilities, they MAY discover another arrangement involving locked
wheels that is also interesting. It explains one of the safety features
that appeared in cars starting around the early 60's (I believe) to address
the problem that occurs when one of the brakelines ruptures and spews brake
fluid all over the place.
Physics can be useful in so many ways.
Cheers!
ron
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