Two uniform planks, each of mass m = 4.05 kg and length L = 2.17 m, are connecte

Question

Two uniform planks, each of mass m = 4.05 kg and length L = 2.17 m, 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. If the chain has the length 0.75 m, find each of the following:

a) the absolute value of the tension in the chain,

b) the absolute magnitude of the force on the hinge of each plank, and

c) the force of the ground on each plank.

Explanation / Answer

taking both the planks together and making its free body diagram, we find that the reaction from the ground balances the weight of a plank. hence, ground reaction = m * g taking g = 9.8 m/sec^2 groung reaction = 396.9 N now, we make free body diagram of a single plank from that we will find that normal reaction at the hinge is zero and horizontal reaction is equal to equal to tension in the chain . by considering moment balance of the single plank about the hinge point , we find tension in the chain equal to tension = mg* tan x , where 2x is the angle between the planks x comes out to be 20.22 degrees hence, tension = 146.19 N reaction at the hinge is equal to tension in the chain , hence , hinge reaction = 146.19 N

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