Torque on a 200 kg plank held by a string: why is my answer twice the book's?

[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

 

[dextercioby]

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

Daniel.

 

[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?

 

[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.

 

[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?

 

[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.

 

[tonix]

That's what I meant to say. Thanks!