Calculating Moment of a Force

The question is the moment of force (torque).

ehild

 

Sorry, I did not notice that you multiplied the force by 2 m. Your answer is correct if the centre of mass of the crate is at 2 m horizontal distance from A. So the figure is not quite correct.

ehild

 

The problem says nothing about the size of the crate. I think you can take that the middle 2 m from A, so 3924 Nm has to be correct.

ehild

 

Is there any more information about how the table is supported by the ground? It seems to me that the question is nearly impossible to answer without more information about the supports A and B. I would assume that A and B are both exerting a verticle force. If A and B are both capable of exerting a moment, then you have 4 unknowns and the system is statically indeterminate. If either is exerting a horizontal force, then I don't think you would even need a moment at A at all. If A (and ONLY A) is able to exert a moment on the system and neither support is giving a horizontal force, then I'm pretty sure your answer is correct, but that seems like a pretty big assumption for them to ask you to make.

Edit: Actually, now that I think about it, I'm pretty sure you can solve it so that A and B are only exerting upward forces, and there's no moment at all. I think either the answer is zero, or the system is statically indeterminate, or you have some very weird table legs that don't offer any upward force.

 

Are you sure there's no implied information, or something they said before about table legs and what support they offer? For example, in my statics class, the prof always drew the supports in a way that we would know exactly what support reactions existed at the support so that she wouldn't have to write it out in the question every time.

I've attached a free body diagram of my interpretation. Even my free body diagram makes some assumptions, and it's still indeterminate. You only have 2 useful equations, but you have three unknowns. The thing is, there's absolutely no reason, based on the information you've given, to assume that the moment at B is zero, so adding that diagram kills it even more. Adding horizontal forces to both legs doesn't really change anything, since they just cancel each other out. That system is indeterminate based on my FBD unless one of the forces/moments shown is zero. Since it seems more reasonable that a table leg would be providing an upward force as opposed to a moment and no upward force, it would make sense to me that the moment at A is zero. That's a pretty poor argument, though, even if it ends up being right.

 

If that's the case, I would argue against it. The assumption that the leg is providing no support is a pretty unreasonable one. If they want you to assume that, then they should have made some indication of that. Can you ask your prof if that assumption is supposed to be made?

 

Oh wait... hold on. I just re-read the question. They want the moment that the crate exerts on point A, not the total moment reaction at A. Wow... I think I just epically failed there. Terribly sorry about that.

In that case, it wouldn't matter whether the moment created by the crate is canceled out by a force at B or a moment at A, it just matters what moment is created by the crate, in which case I don't know what's wrong with your answer. Sorry again for not reading the question properly...

 

Only the moment of the force exerted by the crate around the support A was the question, not the forces exerted by the supports. The crate exerts a normal force, which is equal to its weight and the line of this force passes through the CM of the crate. The mass of the crate is 200 kg, and it is also given that the crate is at 2 m distance from support A. You can ask, which part of the crate is there - the left side, the right side or the middle. If the middle, then it is all right.

ehild