Solve Equilibrium Problem: 4 Men Carrying Beam, Calculate Forces

[yasar1967]

1. Four people carry a uniform beam of length L (with mass M) holding it horizontal. Two men hold it at the ends while the remaining two are inward but nevertheless all men are equally apart from each other i.e. if the beam is 4m long the distance from 1st to 2nd is 1m; 2nd to 3rd is 2m and 3rd to 4th is 1m.
Calculate the normal forces acting upon the men.



2. System is in equilibrium, static. general force and torque formulas apply.



3. I assumed due to symmetry, outward Fn forces and inward Fn forces must be equal. Therefore Mg=2xFno+2xFni
The problem is the SAME equation stems from torque formula as well and as I have two identical formulas with two unknowns, I get nowhere.
Where did I go wrong?

 

[Doc Al]

You didn't go wrong. The problem is statically indeterminate--you just don't have enough information. For example: The two end people can lift 90% of the weight if they want and the two guys in the middle could just pretend to help. That and many other combinations of forces are consistent with the given information.

Of course, you could just assume that the load is evenly distributed.

(Also: If they are evenly spaced and the board is 4m long, they are 4/3 m apart.)

 

[yasar1967]

thank you