Moments - Support forces acting on a rod

[AntSC]

Homework Statement

This is more of a question of applying the correct principles to a range of problems involving a horizontal rod hinged to a wall that is then supported by another rod. The support rod is also attached to the wall from above or below and then attached to the horizontal rod, so it is at some angle to the horizontal direction.
My question is about the forces that act on the horizontal rod from the support rod. If the support rod is attached below the horizontal rod, then the horizontal rod experiences a force supplied by the support rod, which acts parallel to the support rod.
My question is, in addition to the force the force supplied by the support rod, is there also a normal reaction force that also acts on the horizontal rod at the point where the support force is in contact with the horizontal rod?
Any help would be greatly appreciated
I'll also i'll add that I'm not interested in the other forces of weight and the hinge forces in the system. Just what is going at the point where the support rod makes contact with the horizontal rod.

Homework Equations

The Attempt at a Solution

 

[haruspex]

a force supplied by the support rod, which acts parallel to the support rod.

Don't assume it is purely horizontal (it cannot be). Alllow it to be in any direction and deduce it from the equations.

 

[AntSC]

In which direction does the support force act on the horizontal rod? All the problems I'm looking at are giving correct answers only if I assume the support rod is applying a force to the horizontal rod in a direction parallel to the support rod.

 

[haruspex]

In which direction does the support force act on the horizontal rod? All the problems I'm looking at are giving correct answers only if I assume the support rod is applying a force to the horizontal rod in a direction parallel to the support rod.

You wrote that you were not interested in other forces, such as weights of rods. But in fact they are crucial. The force will only be parallel to the support rod if it is weightless.

 

[AntSC]

Thanks for pulling me up on my considerations. I meant to only point out that I just wanted to know what happens at the point of support.
I guess I also didn't mention that this is a statics problem. If so, does that still make the weight of the horizontal rod and the forces where it the horizontal rod attaches to the wall significant in determining the angle of the support force?
Thanks again

 

[haruspex]

does that still make the weight of the horizontal rod and the forces where it the horizontal rod attaches to the wall significant in determining the angle of the support force?

Yes.
Take moments about the hinges where the rods attach to the wall. In each case, the only torques will be from the weight of the same rod and from the reaction force where it joins the other rod. If the first rod is weightless then there can be no torque from the reaction force, so the reaction force must act along that rod.

 

[AntSC]

Hi Haruspex. Taken me ages to reply. Busy time of year!
Following off from your last message, if we assume the main rod is perpendicular to the wall but the support rod is not perpendicular to the main rod, how would I accurately consider all the forces acting on the main rod if I was going to take moments about the hinge?
I have only the main rod's weight and the force supplied by the support rod. Given that the support rod is not acting on the main rod at 90 degrees but at some other angle, how do I model this support force? Does it act perpendicular to the main rod? Does it act in the same direction of the line of the support rod? And is there a reaction force due to the main rod's weight on the support rod? Is this the same as the support rod's force?
I've attached a diagram to illustrate.

 

[kuruman]

Does it act perpendicular to the main rod? Does it act in the same direction of the line of the support rod?

In general the support rod will exert a horizontal and vertical component at the point of contact. Now the resultant of the two will not necessarily be along the rod. The vertical component varies with distance from the pivot. You can see how that is if the horizontal rod is supported by a vertical string from above instead of from below at distance x from the pivot. The tension (and the vertical component supplied by the support rod) is T= mgL/(2x). Of course, the wall provides a vertical component F_y such that T + F_y = mg.

What about the horizontal component? The details of how the support rod makes contact with the horizontal rod cannot be ignored. Suppose you are told that the contact between the support rod and the horizontal rod is frictionless so there can be no horizontal component. Can the horizontal rod be in static equilibrium? Yes, because horizontal forces are not needed to maintain static equilibrium. This assumes that the support rod is firmly screwed to the wall otherwise the net torque on it cannot be zero. A frictionless contact can be simulated by attaching a small wheel at the end of the support rod that's in contact with the horizontal rod. Will the wheel turn?

 

[haruspex]

Does it act in the same direction of the line of the support rod?

As I wrote, it depends whether the support rod is weightless. Let the reaction force be R and the weight W. Take moments about the point where it meets the wall. Only W and R have a moment about that axis so must have equal and opposite torques. If W is zero neither have a torque, so R must be along the line of the rod.
Conversely, if W is nonzero then R must have a component normal to the rod.

The details of how the support rod makes contact with the horizontal rod cannot be ignored. Suppose you are told that the contact between the support rod and the horizontal rod is frictionless so there can be no horizontal component.

As I understand it, the two rods are freely jointed.

 

[kuruman]

As I understand it, the two rods are freely jointed.

Yes, my intention was to indicate that there are more than two possibilities for the direction of the force exerted by the supporting rod.

 

[haruspex]

Yes, my intention was to indicate that there are more than two possibilities for the direction of the force exerted by the supporting rod.

Sorry, I don't get it.
A frictionless joint would just mean that there is no torque transferred at the joint. It does not prevent there being a horizontal component to the force.

 

[kuruman]

Sorry, I did not explain myself very well. I was thinking no joint or hinge at the horizontal rod contact, just support from underneath.