Calculate the forces that the supports A and B exert on the diving board shown i

Question

Calculate the forces that the supports A and B exert on the diving board shown in (Figure 1) when a 56-kg person stands at its tip.

Calculate the force that the support A exerts on the diving board. Ignore the weight of the board.

Calculate the force that the support B exerts on the diving board. Ignore the weight of the board.

Calculate the force that the support A exerts on the diving board. Take into account the board's mass of 29 kg . Assume the board's CG is at its center.

Calculate the force that the support B exerts on the diving board. Take into account the board's mass of 29 kg . Assume the board's CG is at its center.

Explanation / Answer

case first when weight of the board = 0 so

Na + Nb = 56 * 9.8 ......................1 simple force balance

Na * 2 + Nb * 1 = 56*9.8* 2 ...............2 simple torque balance about COM of board

so from 1 & 2 we got

Na = 548.8 N

Nb = 0   

case 2 when board has m= 29 kg

Na + Nb = 56 * 9.8 + 29*9.8 ......................1 simple force balance

Na * 2 + Nb * 1 = 56*9.8* 2 ...............2 simple torque balance about COM of board

from 1& 2 we got

Na = 264.6 N
Nb =568.4 N

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