Question

34. A uniform ladder of mass m rests against a frictionless vertical wall at an angle of 60°. The lower endth mass M=2m attempts to climb the ladder. What fraction of the length L of the ladder will
the student have reached when the ladder begins to slip?

Answer 1

$H/V=0.4\to H=0.4V$

$H=F$

$V-mg-2mg=0\to V=3mg$

$H=0.4\cdot3mg=1.2mg$

$-mg(L/2)\cos60°-2mgx\cos60°+1.2mgL\sin60°=0$

$-(L/2)\cos60°-2x\cos60°+1.2L\sin60°=0$

$-L/4-x+1.039L=0\to\frac{x}{L}=0.789$

So,

$x\approx79\%$ of $L$.