A diving board length L = 5.00 m that weighs 235 N is supported by two pillars.

Question

A diving board length L = 5.00 m that weighs 235 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 = 1.60 m away(Figure 1)

Part A

Find the direction of the force exerted by the left pillar when a 85.0 kg diver stands at the far end of the board (upward or downward)

Part B

Find the magnitude of the force exerted by the left pillar when a 85.0 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 85.0 kg diver stands at the far end of the board.(upward or downward)

Explanation / Answer

T_cc = Counterclockwise torque
T_cw = Clockwise torque
r = distance from point of rotation
m = mass diver = 85 kg
g = gravity = 9.8 m/s^2
Wb = weight of board = 235 N
Wd = weight of diver = m * g = 85kg * 9.8m/s^2 = 833.85 N
F_l = force left pillar
F_r = force right pillar

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
3.4m * 833.35 N + 0.9m * 235N = 1.7m * F_l
F_l = 1791.12 N
Thus, the left pillar exerts a force of 1791.12N downward or counterclockwise.

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
5m * 833.35N + 2.5m * 235 N = 1.7m * F_r
F_l = 2796.6 N
Thus, the right pillar exerts a force of 2796.6N upwards or counterclockwise.

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