Question

81. . . A 67.0-kg person stands on a lightweight diving board supported by two pillars one at the end of the board, the other 1.10 m away. The pillar at the end of the board exerts a downward force of 828 N. (a) How far from that pillar is the person standing? (b) Find the force exerted by the second pillar.

Answer 1

The diving board is a cantilever. There are two forces downward - the pillar at the end of the board and the force

presented by the person who is standing on the opposite side of the center pillar.

Force presented by the person = mg = 67 kg x 9.81 m/s^2 = 657.27 N

b)

The force exerted by the second pillar must equal the sum of the forces from the first pillar (at the end of the board)

and from the person as the whole system is stationary.

= 657.27 + 828 = 1485.27 N upwards.

a)

As the system is stationary, we consider that the forces are rotating about the first pillar (at the end of the board).

Let d be the distance the person is from the pillar the end of the board

d x 657.27 = 1.10 x 1485.27 N

d = 1633.797 / 657.27

d = 2.486 m