A diver of weight 690 N stands at the end of a diving board of length L = 4 m an

Question

A diver of weight 690 N stands at the end of a diving board of length L = 4 m and negligible mass. The board is fixed to two pedestals separated by distance d = 1.5 m.

(a,b) What are the magnitude and direction of the force on the board from the left pedestal? (Include the sign. Take upward to be positive.)
N

(c,d) What are the magnitude and direction of the force on the board from the right pedestal? (Include the sign. Take upward to be positive.)
N
(e,f) Which pedestal is being stretched and which is being compressed?

The left pedestal is being stretched.The right pedestal is being stretched.The left pedestal is being compressed.The right pedestal is being compressed.

Explanation / Answer

We take the force of the left pedestal to be F1 at x = 0, where the x axis is along the diving board. We
take the force of the right pedestal to be F2 and denote its position as x = d. W is the weight of the diver,
located at x = L. The following two equations result from setting the sum of forces equal to zero (with
upward positive), and the sum of torques (about x2) equal to zero:

F1 + F2 -W =0

F1*d + W( L - d ) = 0

(a) The second equation gives

F1 = - ( L - d) * W / d = - 1150 N

(b) F1 is negative, indicating that this force is downward.

(c) The first equation gives F2 = W - F1 = 690 + 1150 = 1840 N

(d) The result is positive, indicating that this force is upward.

(e) The force of the diving board on the left pedestal is upward (opposite to the force of the pedestal on
the diving board), so this pedestal is being stretched.

(f) The force of the diving board on the right pedestal is downward, so this pedestal is being
compressed.

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