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## Homework Statement

Hello, I have a problem I don't want how to approach, it is a little weird. It is a problem of equilibrium (torque)

The situation and my approach is in the picture I uploaded. A beam is supported by the blue structure. On the beam it is a person(100N) at a distance of 3m in

the overhang part. In order to avoid that the beam turns over, it is placed a counterweight of mass M in the middle of the supported part. The goal is to find

the needed mass of the counterweight.

Any help will be greatly appreciated.

## Homework Equations

T net=0

Fy net=0

## The Attempt at a Solution

My approach: Since 2m of the beam is supported by a structure, I think the structure will produce a distrubuted load of reaction, but that does not matter since we can

use use a single reaction in the middle of the distributed load ( at 1m from the end in this case, as I showed in the figure). The problem is the next:

If I apply torque in the red point ( the point under the counterweight), only the 100N will excert a torque, which is wrong because the system must be in equilibrium.

I would get that -400 N.m =0

If I apply torque in the blue point (at the right end of the blue support structure), all forces will excert torque. I set up my equation and I got -300-R-M=0

Then I find the second equation with the summation of forces, and I got R=100+M. For last I replaced this last equaqtion into the first to find M.

But again I got -400 N.m = 0.

I do not think I've forgotten some reaction force somewhere ... I am thinking right now that I don't have to take into account that reaction force in that way, because once the beam starts to turn over, the normal force (reaction force) will vanish. I meant, I will only have a reaction force in the "pivot ( blue point

in the drawing)". In that case the problem will be very easy to solve, but I am not sure of that approach. The second image I uploaded shows that approach.

Any help will be greatly appreciated.