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A 10 m beam of mass 290 kg extends over a ledge. The beam is not attached, but simply rests on the surface. A 80 kg student intends to position the beam so that he can walk to the end of it. How far from the edge of the ledge can the beam extend?

Added Sat, 06 Jun '15

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First, draw a free body diagram.

Our givens :

M = 290kg = Mass of Beam

m = 80kg = mass of Student

L = 10M = length of beam

P = pivot point.

x = length of beam extended.

Then, set up our equilibrium equations.

Tq = Mg*(5-x) - mg * x + F*0 = 0

>> Mg(5-x) = mg*x

Now solve for X

>> 5Mg - xMg = xmg

>> 5Mg = x(M+m)

>> 5M / (M + m) = x

Now plug in your Variables.

5M / (M + m) = x

5(290) / (290 + 80) = x

3.918 = x = distance the beam can extend for a 80kg student to walk to the end.

When you actually do this problem, don't forget the units.

I excluded them above because m for meters would be confusing with the previously defined variables.

Carrying through your units is one of the most effective checking methods there is.

Added Sat, 06 Jun '15

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