Tasha has a mass of 20 kg and wants to use a 4.0 m board of mass 10 kg as a sees

Question

Tasha has a mass of 20 kg and wants to use a 4.0 m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board. How far is she from the support point?

I am really having trouble visualizing this problem. I understand that normally for a 4 m board, the center of gravity would be at 2 m. I am just confused about the support point and would appreciate any help. The answer is said to be 0.67 m. Thank you.

Explanation / Answer

Mass of Tasha, m1 = 20 kg Mass of the board, m2 = 10 kg Distance of Tasha from the end where she sits, x1 = 0 Distance of center of gravity of board from Tasha, x2 = 4/2 = 2 m Centre of gravity of the system = [ ( m1 x1 + m2 x2 ) / ( m1 + m2 ) ] = [ ( 20 * 0 + 10 * 2 ) / ( 20 + 10 ) ] = 20 / 30 = 0.67 m Distance of Tasha from support = Distance of centre of gravity from Tasha = 0.67 m

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