Help with Elasticity question
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Help with Elasticity question

[From: ] [author: ] [Date: 12-04-19] [Hit: ]
Having calculated the shear strain, check whether it is greater than or less than the given breaking strain.(If its greater, the bone will break.......
A person of mass 100kg running at 6m/s is tackled and brought to a halt in 0.1s. The impact of the tackle is absorbed by one of his legs only, by the shearing of a particular bone of cross-sectional area 3x10^-4 m^2. If the shear modulus of bone is 10^10 N/m^2, and the breaking strain is 10^-3, calculate whether or not the bone will be broken.

Please show how you worked out the answer. Thanks in advance!

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First, figure out the force of the impact:

F = ma = m(Δv/t)

For "m", use 100kg; for "Δv" use 6 meters/sec; for "t" use 0.1s

The shear modulus ("G") equals the shear stress divided by the shear strain:

G = (shear stress) / (shear strain)

The shear stress is the force divided by the cross-sectional area:

G = (F/A) / (shear strain)

Solve for shear strain:

shear strain = (F/A) / G

Calculate the shear strain. For "F", use the value you calculated above. For "A", use 3×10^-4 meter². For "G", use 10^10 N/meter².

Having calculated the shear strain, check whether it is greater than or less than the given breaking strain. (If it's greater, the bone will break.)
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