A horizontal 40 N board of uniform density supports two children weighing 500 N

Question

A horizontal 40 N board of uniform density supports two children weighing 500 N and 350 N. The support or fulcrum (the point about which rotation would occur if forces and torques were not balanced) is under the center of gravity of the board and the 500 N child is 1.5 m from the fulcrum. (a) Determine the upward force N that is exerted on the board by the support. (b) Where should the 350 N child sit to balance the system? (c) Now permit that the axis of rotation be through the center of mass of the 500 N child, but parallel to the original axis of rotation. Again calculate where the 350 N child should sit to balance the system.

Explanation / Answer

a )

F = 500 + 40 + 350

F = 540 + 350

F = 890 N

b )

350 x = 500 X 1.5

x = 500 X 1.5 / 350

x = 750 / 350

x = 2.142 m

c )

same as of the above value of distance

x = 2.142 m

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