A diving board length L = 5.20 m that weighs 240 N is supported by two pillars.

Question

A diving board length L = 5.20 m that weighs 240 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 = 1.65 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.

ans. 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.

ans. upward

art D

Find the magnitude of the force exerted by the right pillar when a 85.0 kg diver stands at the far end of the board.

Explanation / Answer

I'll do (c & d) first since I'd like to sum the moments about the left end. That will give me the force under the right pillar.
M = 0 = R * 1.65m - 240N * 5.20m/2 - 85.0kg * 9.8m/s² * 5.20m
R * 1.65m = 4955.6 N·m
R = 3003.39 N force under right pillar

(a & b) To find the force at the left pillar, just sum the vertical forces:
F = 0 = L + R - mg
0 = L + 3003.39N - 85.0kg * 9.8m/s²
L = -2170.39 N left pillar
The sign tells us that this force acts downward.

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