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If you jump from a height of only 2m above the ground and land without bending your legs, the bones in your lower legs will break due to the compression they experience.

The tensile strength of bone is 100 x 106 N/m², and the total cross-sectional area of the bones in your lower legs is 50 mm².

(a) Calculate the force that needs to be applied to the lower leg bones before they break.

(b) The bones in the lower leg are approximately 40 cm long. Use the stress-strain
relationship to estimate how much the bones are compressed as they reach breaking
point. The Young's modulus of bone is 1.6 x 1010 N/m². (8 points)

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Answer:

(a) 5000 N

(b) 0.25 cm

Explanation:

(a)

Tensile strength is given by [tex]\frac {F}{A}[/tex] where F is force and A is area

F=Area* Tensile strength

[tex]F=100*10^{6}*50*10^{-6}=5000 N[/tex]

Therefore, F=5000 N

(b)

Young’s modulus, [tex]E=\frac {stress}{strain}[/tex]

[tex]Strain=\frac {\triangle l}{l}[/tex] where [tex]\triangle l[/tex] is elongation and l is original length

[tex]\triangle l=\frac {100*10^{6}*40*10^{-2}}{1.6*10^{10}=2.5*10^{-4} m[/tex]

[tex]\triangle l=0.25 cm[/tex]

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