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

  • Thread starter Ryker
  • Start date
1,086
2
1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Torque and force equilibrium.

Tension force + normal force = weight of person.

3. 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?
 

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