Two uniform planks, each of mass m and length L, are connected by a hinge at the

Question

Two uniform planks, each of mass m and length L, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape of an A, on a frictionless surface without collapsing. As a function of the length of the chain, find:

a) the tension in the chain
b) the force on the hinge of each plank
c) the force of the ground on each plank

*My attempt for part a is ____> (mg(sqrt(L^2+l^2)))/l ? (mass times gravity times the square root of L squared plus l squared, all over l)

Explanation / Answer

N = m g normal force on each plank since surface is frictionless This is also the force of the ground on the each plank Take torque about hinge N L cos theta = T L sin theta / 2 theta is angle plank makes with surface N = T sin theta / (2 cos theta) T = 2 N / tan theta = 2 m g / tan theta The hinge can exert only a horizontal force on the planks otherwise the normal force would differ from the weight of a plank Now take torque about the contact with the ground F L sin theta = L/2 T sin theta F = T/2 force of hinge on each plank

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