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## Main Question or Discussion Point

This is a problem posted by a member on Brilliant.org (https://brilliant.org/problems/acceleration-of-hinges/). I found one way to solve the problem, but it is really long, and i am looking for some different solutions. The problem is-

Four similar rods of uniform density are connected with frictionless hinges. This frame is placed on a horizontal smooth tabletop, such that its shape is a square. Vertex P is acted upon by a horizontal force in the direction of the diagonal, and due to this force it begins to move at an acceleration of ##a_P##.

If the initial acceleration of the opposite vertex Q is ##a_Q= k.a_P## then find k.

k is positive if Q moves away from P and k is negative if Q moves closer to P.

Please post any solution or approach that can be applied in it.

Thanks.

Four similar rods of uniform density are connected with frictionless hinges. This frame is placed on a horizontal smooth tabletop, such that its shape is a square. Vertex P is acted upon by a horizontal force in the direction of the diagonal, and due to this force it begins to move at an acceleration of ##a_P##.

If the initial acceleration of the opposite vertex Q is ##a_Q= k.a_P## then find k.

k is positive if Q moves away from P and k is negative if Q moves closer to P.

Please post any solution or approach that can be applied in it.

Thanks.