From: Tom Woosnam (twoos@csus.com)
Date: Sat Nov 16 2002 - 09:47:21 PST
Message-id: <fc.000f5b5a0080de273b9aca0027a60c0d.80de43@csus.com> Date: Sat, 16 Nov 2002 09:47:21 -0800 Subject: Re: Pinhole Digest #1061 - 11/16/02 From: "Tom Woosnam" <twoos@csus.com>
Marc,
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
pinhole@exploratorium.edu writes:
>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).
Tom Woosnam
Chair, Science Dpt.
Crystal Springs Uplands School
400 Uplands Drive
Hillsborough CA 94010
(650) 342 4175 x 1502
FAX (650) 342 7623
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