A uniform ladder of mass M and length L stands on rough horizontal ground and le

Question

A uniform ladder of mass M and length L stands on rough horizontal ground and leans against a
smooth vertical wall with which it makes an angle ?. A man of mass m stands on the ladder a distance
x from the bottom.
(a) Obtain expressions for the normal reaction and the friction force acting at the point of contact
between the ladder and the ground.
(b) If the coefficient of friction at this point is 1/3, show that only if tan? < 6/17 is the man able to
reach the top of the ladder without it slipping. Use M = 10kg, m = 80kg and L = 4m.

Explanation / Answer

a)the forces acting at contact point (on ground)
i) normal force N1vertically upward
ii) frictional force f1 towards right(ladder is leaning against the wall on right side)
b) forces acting at mid point of the ladder
i)its weight Mg vertically downward
c) forces acting at upper contact point
i)frictional force f2vertically upward f2=0(wall is frictionless)
ii)normal force N2 towards left

iii)weight of the person=mg vertically downward

net Fy=0
N1=Mg+mg
f1=N1=(M+m)g=(M+m)g/3
net Fx=0

f1-N2=0
f1=N2

(M+m)g/3=N2

about y-axis net torque=N1*0-Mg*0.5L-mg*L=0

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