Question

What is the actual frictional force when the man has climbed $1.0$ m along the ladder?

• A. $360N$
• B. $171N$
• C. $900N$
• D. $740N$

Answer 1

Answer: (B)

$171N$

At the point on the vertical wall there is normal force along horizontal direction and at the ground there will be normal force in vertical direction and friction force in horizontal direction.
Weight of Ladder is acting at 1.5m from ground contact point and is 160 N (downwards) in vertical direction and Weight of man is acting at (3/5)x1=0.6m from ground contact and is 740 N (downwards) in vertical direction
Net torque about ground is zero,
$740\times 0.6+160\times 1.5-N_H\times 4=0N_H=171N$
By doing Force Balance along horizontal we get Friction force=Normal Horizontal= 171N
Just to check whether friction can be upto 171N or not.
$N_V=740+160=900N{F}_{max}=900\times 0.4=360N$
As max value of friction can be upto 360N so our answer 171N is correct