Question

A person (40 kg) is managing to be at rest between two vertical walls by pressing one wall B by his back (figure). Assume that the friction coefficient between his body and the walls is 0.8 and that limiting friction acts at all the contacts.
(a) Show that the person pushes the two walls with equal force.
(b) Find the normal force exerted by either wall on the person. Take $g=101m/s^2$

Answer 1

Mass of man = 50kg. g = 10 m/s²
Frictional force developed between hands, legs & back side with the wall the wt of man. So he remains in equilibrium. He gives equal force on both the walls so gets equal reaction R from both the walls. If he applies unequal forces R should be different he can’t rest between the walls. Frictional force 2μR balance his wt.
From the free body diagram

$\mu R+\mu R=40g=2\mu R=40\times 10=R=\frac{40\times 10}{2\times 0.8}=250N$

the normal force is 250N