Evil torque problem

1. Jan 15, 2005

tonix

Hi

I have a problem for which the given solution makes no sense to me.

A 200 kg plank of length 2m is attached by a hinge at one of its ends to a wall. It is held in place horizontally by a string. The string breaks and I am supposed to find the torque at that point. (See attached image).

I have that torque = r x F which gives me a torque vector with a magnitude of 9.8 m/s^2 * 2m * 200kg = 3920 Nm.
The solution the book gives, however, is half of that, ie 1960Nm.

Could somebody either reassure me that the book is wrong or clarify where I made a mistake?

Thank you,
tonix

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2. Jan 15, 2005

dextercioby

Can u see why your answer is twice more??Is it F,or is it "r"??

Daniel.

3. Jan 15, 2005

tonix

Well, I don't know why it is twice more. That is the problem. It seems that r should be 2m for sure. I suppose it could be F since the gravity is only acting on half the mass?

4. Jan 15, 2005

dextercioby

Nope,gravity affects all mass...Think about the point of application of the gravity force and its whereabouts wrt the rotation point of the rod...

Daniel.

5. Jan 15, 2005

tonix

ahh... so the overall point of application of the gravity force is in the middle of the rod and therefore r is only 1m instead of 2m?

6. Jan 15, 2005

dextercioby

It's actually in the center of mass,but,assuming the mass is distributed uniformly throughout the rod,it would be exactly at the middle.
Yes,that distance is only of 1 meter.

Daniel.

7. Jan 15, 2005

tonix

That's what I meant to say. Thanks!