How Does a Gymnast Affect the Forces on a Balance Beam?

[ctwokay]

Homework Statement

A gymnast with mass m1 = 48 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 119 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
Now the gymnast (not holding any additional mass) walks directly above the right support.
Q1:What is the force the left support exerts on the beam?
Q2:What is the force the right support exerts on the beam?

Homework Equations

$\Sigma$F=0
τ=0

The Attempt at a Solution

For q1 I have used m1*g+m2*g - 3(m1+m2/2)*g is this correct?
For q2 is 3(m1+m2/2)*g is this correct?

 

[anathema]

Hello,

Thank you for your post.

For Q1, your equation is not quite correct. The left support will exert a force on the beam, but the gymnast is also exerting a force on the beam as they walk above the right support. This will cause a torque on the beam, so the left support will have to exert a force to counteract this torque and keep the beam in equilibrium.

The correct equation for Q1 would be: ΣF = m1*g + m2*g - Fleft = 0

Where Fleft is the force exerted by the left support. This can be solved for Fleft to find the answer to Q1.

For Q2, your equation is correct. The right support will only have to exert a force equal to the weight of the beam (3/2 * m1 + m2) to keep it in equilibrium.

I hope this helps. Keep up the good work!