A diving board length L = 5.20 m that weighs 250 N is supported by two pillars.

Question

A diving board length L = 5.20 m that weighs 250 N is supported by two pillars. One pillar is at the left end of the diving board, as shown below; the other is distance d = 1.50 m away(Figure 1) .

Part A

Find the direction of the force exerted by the left pillar when a 90.0 kg diver stands at the far end of the board.

Part B

Find the magnitude of the force exerted by the left pillar when a 90.0 kg diver stands at the far end of the board.

Part C

Find the direction of the force exerted by the right pillar when a 90.0 kg diver stands at the far end of the board.

Part D

Find the magnitude of the force exerted by the right pillar when a 90.0 kg diver stands at the far end of the board.

Explanation / Answer

T_cc = Counterclockwise torque
T_cw = Clockwise torque
r = distance from point of rotation
m = mass diver = 90kg
g = gravity = 9.8m/s^2
Wb = weight of board = 250N
Wd = weight of diver = m * g = 90kg * 9.8m/s^2 = 882N
F_l = force left pillar
F_r = force right pillar

A) The left pillar exerts a force of 2342.27 N downward or counterclockwise.

B) When considering force by the left pillar, consider the right pillar as the point of rotation:
T_cc = T_cw
r * Wd + r * Wb = r * F_l
3.7m * 882N + 1m * 250N = 1.5m * F_l
F_l = 2342.27 N

C) The right pillar exerts a force of 3474.27 N upwards or counterclockwise.

D) When considering force by the right pillar, consider the left pillar as the point of rotation:
T_cc = T_cw
r * Wd + r * Wb = r * F_r
5.2m * 882N + 2.5m * 250N = 1.5m * F_r
F_l =3474.27 N

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