How Far Can a Man Stand on a Horizontal Beam Without Falling?

[gnsdraw]

Standing on a horizontal beam!

|\
| \
| \ rope
| \
| \
|wall \
| \
|...beam...37*
x |w

a beam is being held up by the rope due to the friction of the wall. the beam has a weight W, and a man is standing x distance away from the wall. the coefficient of friction with the wall is 1/2, the angle is 37*. what is the maximum distance towards the wall that the man can stand without falling.

i don't know how to start, the only thing i can think of is to use the torque at the angle =[

 

[lippyka]

The maximum distance the man can stand without falling can be found by using the equation for static equilibrium: Fnet = 0 TsubW + Tsuba = 0 Where TsubW is the torque due to the weight of the beam and Tsuba is the torque due to the friction between the wall and the beam. TsubW = W*x Tsuba = 1/2 * W * x * cos(37) Solving for x, we get: x = (2*TsubW)/(W*cos(37)) Therefore, the maximum distance the man can stand without falling is: xmax = (2*W)/(W*cos(37)) = 2/cos(37)