Torque Due to Weight Video Lessons

Concept

# Problem: A gymnast with mass m1= 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2= 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 beamb. at the right supportc. at the right edge of the beam

###### FREE Expert Solution

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:

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

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 FL and FR on the beam.

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###### Problem Details

A gymnast with mass m1= 46 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2= 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