Question

A plank 2.00 cm thick and 14.3 cm wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends 2.00 m horizontally over the sea below. A man of mass 95.3 kg is forced to stand on the very end. If the end of the board drops by 4.90 cm because of the man's weight, find the shear modulus of the wood.

Answer 1

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A plank 2.00 cm thick and 17.9 cm wide isfirmly attached to the railing of a ship by clamps so that the restof the board extends 2.00 m horizontally over the sea below. A manof mass 85.3 kg is forced to stand on thevery end. If the end of the board drops by 6.00 cm because of the man's weight, find the shearmodulus of the wood.

Answer

Shearing stress is given as

      Stress = F /A

                = m g /A           ( F = m g, which is the weight of theman)

                = m g / ( d x w )

here d is the thickness and w is the width. Sostress

               = (85.3)(9.8) / ( 0.02 x 0.179m)

                = 2.335x10⁵ Pa

      Shearing strain is givenas

               ? = ? L / L

                   = 0.06m / 2 m

                  = 0.03

Shear modulus of wood is

           = stress / strain

           = 2.335x10⁵ Pa   / 0.03

           = 7.7834x10⁶ Pa