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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?

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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

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.
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