A seesaw consisting of a uniform board of mass M and length L, supports at rest a father and daughter with masses "mf " and "md", respectively.

The support (called the fulcrum) is under the centre of gravity of the board, the father is the distance "d" from the center and the daughter is a distance "L/2" from the center.

A) determine the magnitude of the upward force "n" exerted by the support on the board?

B) determine where the father should sit to balance the system at rest?

A) N = (M + mf + md) g

B) d = md L / (2 mf)

Explanation:

Draw a free body diagram. There are four forces acting on the board.

Weight force M g pulling down at the center of the board.

Normal force N pushing up at the center of the board.

Weight force mf g pulling down a distance d from the center.

Weight force md g pulling down at the end of the board.

Sum of forces in the y direction:

∑F = ma

N - M g - mf g - md g = 0

N = (M + mf + md) g

Sum of moments about the center of the board:

∑τ = Iα

md (L/2) - mf d = 0

d = md L / (2 mf)