Tension on two chains holding a board

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The discussion revolves around calculating the tension in two chains supporting a horizontal board with a person sitting on it. The board weighs 125 N and is 4 m long, while the person weighs 500 N. Participants emphasize the importance of drawing a free body diagram and applying the equilibrium condition, where the sum of vertical forces must equal zero. There is confusion about how to determine the tension in the chains without knowing the person's position on the board. Ultimately, the conversation highlights the need to analyze forces and moments to find the unknown tensions accurately.
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Homework Statement



A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. A person weighting 500 N is sitting on the board. The tension in the right chain is:

a) 250 N
b) 375 N
c) 500 N
d) 625 N
e) 875 N

How far is the person from the left end of the board?
a) .4 m
b) 1.5 m
c) 2 m
d) 2.5 m
e) 3 m

I really have no idea how to do this one; wouldn't you have to know how far the person is from one of the sides first to know what the tension is on one side?

This is my first post here, so I hope I didn't do something wrong :)
 
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Start by drawing a free body diagram and then use the fact that the board is in equilibrium.
 
So the body is 500 N downwards, while the 250 N tension, the unknown tension of the second chain, and the 125 N board all oppose it, and the fact that it's in equilibrium means that the sum of all the net forces is 0, but what after that?
 
Physsics said:
So the body is 500 N downwards, while the 250 N tension, the unknown tension of the second chain, and the 125 N board all oppose it, and the fact that it's in equilibrium means that the sum of all the net forces is 0, but what after that?

How did you get the tension in the left chain?
 
I didn't, I just said that one of the chains (presumably the right chain) has a tension of 250 N.
 
Physsics said:
I didn't, I just said that one of the chains (presumably the right chain) has a tension of 250 N.

Well you'd have the two weights downwards and the two tensions upwards. Then you should be able to use ∑Fy=0 to get the tensions as they should be the same.
 
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