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!
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.)
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.)