Problem: From what maximum height can a 75 kg person jump w/obreaking the lower leg bone on either leg? Ignore air resistance and assume the CM of the

Efan Halliday

Efan Halliday

Answered question

2021-04-24

Problem: From what maximum height can a 75 kg person jump w/obreaking the lower leg bone on either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60m from the standing to the seat position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is 170×106 Nm2 and its smallest cross sectional areais 2.5×104

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-04-26Added 75 answers

The maximum force that each leg can withstand before breaking
F=PA 
=4.25104 N 
If there is even landing with both feet, the max force exerted on the body 
F=8.50104 N 
Finding the landing speed using the work-energy principle, we have
0=DK+DU 
=(12mvl and 20)+(0mghmax) 
Or v12=2ghmax 
Considering the impulse's positive direction
Fmaxt=mDv 
=m(0vI) 
Or t=mvIFmax 
For the landing we have using the equation of motion ( as force is constant, acceleration is constant) 
y=vIt+12at2 
substituting for t from equation we get 
y=vI(mvIF)+12(Fm)(mvIF)2 
=(12)mvI2F 
substituting for vl from equation and simplifying we get 
y=mghmaxF 
Or hmax=Fymg 
hmax=70m

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