Question

A 66 kg adult sits at one end of a 9.2 m long board. His 29 kg child sits on the other end.

A) Where should the pivot be placed so that the board is balanced, ignoring the board's mass?

B) Find the pivot point if the board is uniform and has a mass of 17 kg .

Answer #1

To balance the board when both of them sit, the pivot point must be at the middle of the mass of the Boarc+Adult+child system. We use this concept to solve. We assume that the adult is sitting at the origin. If the location of the child is (x,y). From given information, we know that (x,y) = (9.2, 0). This gives us

This is the location of COM for the first case.

If the board also has a mass and is of uniform density, then the middle of the mass of the board would be at its geometric middle. It is at (4.6,0). We calculate COM using the below

This is the COM if the board has a mass.

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