In this problem, we are dealing with forces. The forces create torques about some points. Thus, we'll be looking into torques and forces.

Torque:

$\overline{){\mathit{\tau}}{\mathbf{=}}{\mathit{r}}{\mathit{F}}}$

Sum of torques for a system in equilibrium:

$\overline{){\mathbf{\Sigma}}{\mathbf{\tau}}{\mathbf{=}}{\mathbf{0}}}$

Sum of forces for a system in Equilibrium:

$\overline{){\mathbf{\Sigma F}}{\mathbf{=}}{\mathbf{0}}}$

We'll also draw a diagram of the situation.

The beams exert upward forces F_{L} and F_{R} on the beam.

A gymnast with mass m_{1}= 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m_{2}= 116 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.

1)What is the force the left support exerts on the beam?

2) What is the force the right support exerts on the beam?

3)How much extra mass could the gymnast hold before the beam begins to tip?

4)Now the gymnast (not holding any additional mass) walks directly above the right support.

What is the force the left support exerts on the beam?

5)What is the force the right support exerts on the beam?

6)At what location does the gymnast need to stand to maximize the force on the right support?

a. at the center of the beam

b. at the right support

c. at the right edge of the beam

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Torque Due to Weight concept. You can view video lessons to learn Torque Due to Weight. Or if you need more Torque Due to Weight practice, you can also practice Torque Due to Weight practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Stelzer's class at UIUC.