Moments Question/Problem

[Jimmy87]

Homework Statement

A plank of wood is attached onto the wall by a hinge. The blank is inclined at an angle of 30 degrees to the horizontal and is held stationary by a rope which is attached at the opposite end onto the wall. Label the three forces acting on the plank

Homework Equations

None

The Attempt at a Solution

I have attached a diagram I have drawn of the problem and my attempt. The tension and weight force are easy but the I am unsure about the third force exerted by the hinge/wall. The answer in the back of the book says that the third force is "the reaction force from the hinge/wall passing through the point where the weight arrow meets the tension arrow". I have no idea what or where this point is they are on about. I approached it by arguing that the hinge must exert equal and opposite forces to the weight and tension. I have drawn a vector diagram on the attachment to and labelled the third force. Is this correct and can someone please explain what this point is they are on about - there is no point where they cross?

Thanks!

 

[haruspex]

Your diagrams are good.
The reasoning in the text is as follows:
Continue the line of action of the weight upwards to where it intersects the rope. Consider moments about the point intersection. Since the rope's tension and the weight both pass through this point, they have no moment about it. The hinge reaction being the only other force on the plank must therefore also have no moment about that point, so must also pass through it.

 

[Jimmy87]

Your diagrams are good.
The reasoning in the text is as follows:
Continue the line of action of the weight upwards to where it intersects the rope. Consider moments about the point intersection. Since the rope's tension and the weight both pass through this point, they have no moment about it. The hinge reaction being the only other force on the plank must therefore also have no moment about that point, so must also pass through it.

Thanks for your help. I have read over what you have said several times and I sort of get it but that line of thinking is really abstract to me. How can you take moments about an imaginary point in space? Have you got any tips about how to approach this type of question as I would never arrive along the line of thinking you have given and using my line of thinking would only give the rough direction of the force from the hinge and not an exact one?

 

[haruspex]

How can you take moments about an imaginary point in space?

Moments are always taken about some point in space. It's just that you are used to that point corresponding to some identifiable point on the rigid body, such as where it experiences a force from another.
In general, it does not matter what (fixed) point you take moments about. When combined with the two usual linear force equations (three if in three dimensions) the same answer can be obtained. But some reference points are more convenient than others.
For more information see https://www.physicsforums.com/insights/frequently-made-errors-mechanics-moments/

 

[Jimmy87]

Moments are always taken about some point in space. It's just that you are used to that point corresponding to some identifiable point on the rigid body, such as where it experiences a force from another.
In general, it does not matter what (fixed) point you take moments about. When combined with the two usual linear force equations (three if in three dimensions) the same answer can be obtained. But some reference points are more convenient than others.
For more information see https://www.physicsforums.com/insights/frequently-made-errors-mechanics-moments/

I get the general idea and I can see how it works but the actual idea itself just seems reaaly strange. That intersection point you mention involves talking about the weight force acting through it and I don't see how the weight force can act through it because the weight force comes from the plank which is nowhere near or touching that point? I guess it is one of those things you just accept works. Thanks for your help anyway, much appreciated - I can definitely follow what you are saying just not how it can work but I can see it does work as you get the right answer!

 

[haruspex]

I don't see how the weight force can act through it because the weight force comes from the plank which is nowhere near or touching that point

Read section 1 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/