Rigid Body Equilibrium problem (no calculus)

[minhaitran]

Homework Statement

Consider a gymnast on a bean placed on upright posts. The beam has a mass of 10kg and the gymnast has a mass of 50kg. The beam is 5 meters long, and the gymnast is 1 meter from the right side. The gymnast may be treated as a particle.

Find the force exerted by each support on the beam. There are two unknowns in the problem, and thus we need two equations.

 

[Fightfish]

Principle of moments. Take moments about each support - the force exerted by that particular support would thus be excluded from consideration.

 

[minhaitran]

Principle of moments. Take moments about each support - the force exerted by that particular support would thus be excluded from consideration.

So how will that help me find the force on that support?

 

[Fightfish]

You can either:
1) Take moments about each support (which will yield the normal force on the other support) or
2) Take moment about one support to get the answer for the other support, and then use translational equilibrium criteria to obtain the force on the first support

 

[SuperCass]

I have a very similar problem.
In this case, what is the lever arm? I know torque = lever arm x force. Is the force the gymnast, or both the gymnast and the beam? Is the beam the lever arm?