Person suspended on a rope standing on a beam (torque and rope tension)

[Ryker]

Homework Statement

A person stands 2.0m from the left fulcrum of a 5.0m-long, 20kg uniform beam. A rope connected to one end of the beam passes up over a pulley, which is right above the person, and down to a harness worn by him. The rope makes a 45° angle with the beam.

Determine the rope tension and the normal force of the beam on an 80kg person.

Homework Equations

Torque and force equilibrium.

Tension force + normal force = weight of person.

The Attempt at a Solution

I figure the tension needs to be the same in both ends of the rope, the one holding the person up and the one holding the beam up. The sum of the moments of force about any point in the beam is zero, because there is no rotational motion. So I took that point to be the point where the person is standing, and then the only two forces acting to cause torque would be the weight of the beam and the force of the rope pulling up said beam.

But I then come up with a paltry figure of 47N for the tension force. But I don't know where I'm going wrong, I mean is the tension not the same throughout the rope? Or does the wall to which the beam is attached exert torque, as well? Because I've tried taking torque at different points, and I come up with different answers for the tension force, which would suggest I am missing something (but I don't know where exactly).

Can anyone offer some help? Where am I going wrong?

 

[anathema]

Hello,

Your approach is correct in terms of considering the forces and moments acting on the beam. However, there are a few things that you may have overlooked in your calculations.

Firstly, the tension force is indeed the same throughout the rope. This is because the rope is assumed to be massless and inextensible, so the tension force is transmitted uniformly throughout its length.

Secondly, the wall to which the beam is attached does indeed exert a torque on the beam. This is because the beam is not attached at its center of mass, so the weight of the beam creates a moment around the point where it is attached. This moment must be balanced by the tension force from the rope.

To solve for the tension force and the normal force, you can set up two equations: one for the sum of forces in the vertical direction and one for the sum of moments around the point where the person is standing. Both equations should equal zero, since the beam is in equilibrium.

Once you have these equations, you can solve for the tension force and the normal force. I hope this helps! Let me know if you have any further questions.