From: Ronald Wong (ronwong@inreach.com)
Date: Fri Nov 15 2002 - 03:40:02 PST
Message-Id: <l03102800b9fa8d17535d@[209.209.18.134]> Date: Fri, 15 Nov 2002 03:40:02 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Center of Mass?
>
>Subject: Center of Mass?
>From: "Marc Afifi" <marc_afifi@yahoo.com>
>Date: Wed, 13 Nov 2002 15:25:32 -0800 (PST)
>
>I should konw the answer to this but I seem to be
>drawing a blank. I have a video demonstration of a
>cart sliding down an inclined plane first with its
>back wheels locked (cart slides down normally) and
>then with its front wheels locked (cart skids around
>until the locked wheels are in back). What's going on?
>Is this a center of mass phenomenon?
>
>-Marc
>
Marc:
What you have here is a classic example of stable and unstable equilibrium
involving the forces parallel to the inclined plane.
When viewed from above the inclined plane with a line of sight
perpendicular to the plane, this is what you would see when the back wheels
are locked up and the car heading straight down the inclined plane:
f f
| ^ ^ |
| | | |
| . |
| C M |
| |
| |
If you draw a line through the CM parallel to the frictional forces, you
will see that the moment arms for both forces about the CM are the same and
therefore the net torque about the CM is zero.
If the car momentarily turns clockwise, the frictional forces will still be
pointing straight up the inclined plane but the moment arm of the left hand
force will now be smaller than that of the right hand force so that there
is a net counterclockwise torque bringing the car back into rotational
equilibrium. In a similar fashion, when the car is momentarily rotated
counterclockwise, a restorative torque is set up in the opposite direction.
This is nothing more than stable equilibrium.
Below is an example when the front wheels are locked and the car is going
straight down the inclined plane.
| |
| |
| . |
| C M |
| f f |
| ^ ^ |
| | | |
| |
Again, the moment arms are equal and there is no net torque about the CM.
But this is a classic example of unstable equilibrium.
Notice that if the car is slightly rotatated about the CM in the clockwise
direction, the moment arm of the left hand force becomes greater than that
of the right hand force and a clockwise torque is created. It's in the same
direction as the initial deviation and, as a result, the clockwise rotation
continues until the locked up wheels end up above the CM as in the first
drawing.
If you have any carts in your classroom, have your kids tape up one set of
wheels so that they can't rotate. They can place their carts one way or the
other to achieve the effect seen in the video. More importantly, they can
play around with their carts to see if there is anything else they might
learn from their experience (what would happens if only one wheel locked
up? What about opposing wheels? Have them predict the results before
testing them to see if they understand what is actually happening).
_____________________________
Steven Eiger's comment:
>...As you brake I always told people that the center of mass moves
>froward.
has to do with rotation in the vertical plane produced by the frictional
forces and is not related to your question.
_____________________________
Cheers!
ron
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