Man connected to harness standing on plank

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Jtwa
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Homework Statement


A professor (m= 75 kg )is seated on a light harness connected to a rope and pulley system. The professor's feet touch a uniform plank (mplank = 15kg) which is supported by a hinge at the wall. A bucket (M) is suspended from the right end of the plank.

m = 75kg
mplank = 15kg
l = 2m
L = 4.9m

Find: Label all the forces on a FBD
Find: T if M=0
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Homework Equations


ΣMhing = 0

The Attempt at a Solution


I took the moment about the hinge and looked at the man by himself. I think I'm drawing my FBD diagram incorrectly.

KpST7JT.png
 
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Hello JT, :welcome:

From your drawing it's clear that the rope is attached to the end of the plank. That should be in the problem statement !

If prof is sitting in the harness, I expect one more force in his FBD. Otherwise I think you have most of it covered. Fry is the only horizontal force I see, so it may well be 0...
 
Have you tried writing the equations for the torques about the hinge end of the plank?
Also, you know that T is constant throughout the length of the rope.
This greatly would simplify the solution since you don't need to consider the forces
acting through the hinge.
 
##T## is the tension in the section of rope above the plank. The section below will have a tension equal to ##Mg## which will generally be different than ##T##, particularly if ##M=0##.
 
Since the rope is connected to the man, why isn't T=(mass of man)*g
 
I'm still having trouble understanding this question. Can someone draw a FBD ? Is Normal Force suppose to be on the FBD?
 
Jtwa said:
I'm still having trouble understanding this question. Can someone draw a FBD ? Is Normal Force suppose to be on the FBD?
An FBD relates to a single rigid body. There are two appropriate FBDs here, one for the man and one for the plank.
Your diagram depicted both, which is ok except that where those two bodies interact you need to show the equal and opposite forces between them.
 
BvU said:
Part of his weight = not all of the weight
It's a question of emphasis in English. If you write that the reason that T is not mg is that part of his weight is taken by the harness it implies that the part taken by the harness accounts for the discrepancy. If you mean that the part not taken by the harness accounts for it then you need to write "only part of his weight...".
 

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