Equilibrium of spiderman

Question

Can spider man hang between those two walls?

(a) Always

(b) Never

(c) If he applies more force on right

(d) If he applies more force on left

Solution

Since the man is in between the walls, to stay hang he have to be in horizontal equilibruim, vertical equilibriun and rotational equilllibruim.

For horizontal equlibrium, reaction force due to hand on the wall and due to leg on the wall should be equal. Therefore option (c) and (d) can't be possible.

For vertical equlibrium, total friction force due to hands and legs should be equal to !!mg!!. Since both the friction coefficients are different, therefore

!!0.1N_1+0.2N_2 = mg!!

But as above !!N_1=N_2!!

!!N_1 = 10/3 mg!!

For rotational equlibrium, net torque due should be zero.

But if you try to find torque about his hands we get.

!!10/3mgxx l-mg xx l/2!!

!!=17/3 mgl!=0!!

So, he is not in rotational equlibrium.

Therefore, he can never hang between the walls.

Therefore option (b) is correct.

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