(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it tipping?

The left post under the very left end of the beam, and the first post is 3.0 m to the right of it. I've attached an image to assist in visualizing.

2. Relevant equations

To be in equilibrium:

[tex]\sum \vec{\tau} = 0[/tex]

[tex]\sum \vec{F} = 0[/tex]

Torque:

[tex]\vec{\tau} = r \cdot \vec{F_\perp}[/tex]

Weight:

[tex]\vec{w} = m \cdot \vec{g}[/tex]

3. The attempt at a solution

Since I know the Torque must be 0 to keep the beam from rotating, I get:

[tex]40 \cdot 9.8 + 20 \cdot 9.8 = 3 \cdot \vec{F}_\text{right beam}[/tex]

3 is the distance from the pivot point (the left beam) to the right beam and F_{2}is force of the right post.

F_{net}must also be 0, so I get the following:

[tex]\vec{F}_\text{left beam} + \vec{F}_\text{right beam} = 40 \cdot 9.8 + 20 \cdot 9.8[/tex]

I'm stuck because I've got 2 functions and 3 unknown variables (F_{left beam}, F_{right beam}, x (distance from the pivot point to the boy)).

I assume there is a way to find these but I'm not sure where to go from here or if I've made a mistake.

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# Homework Help: Problem dealing with Equilibrium & Torque

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