   Chapter 9, Problem 67P

Chapter
Section
Textbook Problem

A plank 2.00 cm thick and 15.0 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 80.0 kg is forced to stand on the very end. If the end of the board drops by 5.00 cm because of the man’s weight, find the shear modulus of the wood.

To determine
The shear modulus of the wood.

Explanation
The shear stress is defined as F/A=S(Δx/h) where S is the shear modulus that is S=(F/A)/(Δx/h) where the force equals the man’s weight F=W=mg .

Given info: Thickness of the plank is 2.00cm , wide of the plank is 15.0cm , mass of the man is 80.0kg , the extension of the board is 2.00m , the drop of the board is 5.00cm , and acceleration due to gravity is 9.80m/s2 .

The formula for the shear modulus is,

S=mghAΔx

• m is mass of the man.
• g is acceleration due to gravity.
• h is the distance between two cross sectional areas the one that directly above the rail and the outer end of the plank.
• A is area of the plank.
• Δx is the drop of the board.

Substitute 80.0kg for m , 9

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