Support reaction on pulley due to cable. Help needed

• kjr
In summary: The net force on the right-hand joint/pulley is then (2T+Tx(1-x))/2, or T+Tx(1-x). In summary, the problem is that you don't know the nature of the support reaction force that the cable exerts by resting on that pulley with load attached. You need to calculate this force.
kjr
Hi and greetings from new member.

A problem brought me to these forums and i am hoping someone will be able to explain what is going on here.

I am working on this project, for which i need to design a truss/frame to support a load. So i came up with this design (diagram attached).

Black is the mounting plate that the whole structure has to be mounted on.
Gray is the simplified metal structure (i didn't draw the crossmembers for simplicity).
Red is the cable, one end attached to the intersection of the frame, then the cable is passed through 2 pulleys (gray circles) and the other end is attached to a hook that the load is attached to.

The intersection acts as a support pulley to hold the cable in place (that's where the problem lies).
The idea is to redirect the force to act into the mounting plate, instead of perpendicular to it, so the frame is more stable and less susceptible to bending and buckling.

Problem is, when i try to do calculations for it, i need to know the nature of the support reaction force that the cable exerts by resting on that pulley with load attached.

Does anyone have any ideas?

Thank you

Attachments

• Truss.png
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kjr: Label all points in your free-body diagram, so it makes it easier to refer to. You might also want to label all dimensions, and draw support reaction forces at each support, if you wish. And you might want to clarify the boundary conditions; i.e., the left-hand end of each gray member is currently shown encased (fixed, welded) to the wall, because no black dot appears at those two attach points. Are the gray members welded to the wall? Or are they pinned at the wall, and therefore free to rotate?

Moving on to your question, the cable exerts three applied loads (they are not called support reaction forces) to the right-hand joint/pulley. Each of the three applied loads is T, each of which is aligned with the three cable lines going to the right-hand joint/pulley. Assuming you have drawn the two left-hand pulleys accurately, and they are really attached to the wall, and not attached to the gray members, then you can replace the cable with three applied forces T, acting on the right-hand joint/pulley. Two of the T forces act at the perimeter of the right-hand pulley, and one of the T forces acts at the black dot.

Last edited:

What is a support reaction on a pulley?

A support reaction on a pulley is the force exerted by a cable on a pulley in order to support the weight of an object hanging from the pulley. It is equal in magnitude but opposite in direction to the weight of the object.

What factors affect the support reaction on a pulley?

The support reaction on a pulley is affected by the weight of the object, the angle of the cable, and the friction between the cable and the pulley.

How do you calculate the support reaction on a pulley?

The support reaction on a pulley can be calculated using the equation R = W/sin(θ), where R is the support reaction, W is the weight of the object, and θ is the angle of the cable.

Why is it important to consider the support reaction on a pulley?

The support reaction on a pulley is important because it determines the tension in the cable, which affects the stability and safety of the system. It also affects the efficiency of the pulley in lifting the object.

Can the support reaction on a pulley be greater than the weight of the object?

No, the support reaction on a pulley cannot be greater than the weight of the object. This is because the pulley is only supporting the weight of the object and not providing any additional force.

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