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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 7 / Problem 10E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: BIO Bone Fractures. The maximum energy that a bone

Chapter 7, Problem 10E

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QUESTION:

Problem 10E

BIO Bone Fractures. The maximum energy that a bone can absorb without breaking depends on characteristics such as its cross-sectional area and elasticity. For healthy human leg bones of approximately 6.0 cm2 cross-sectional area, this energy has been experimentally measured to be about 200 J. (a) From approximately what maximum height could a 60-kg person jump and land rigidly upright on both feet without breaking his legs? (b) You are probably surprised at how small the answer to part (a) is. People obviously jump from much greater heights without breaking their legs. How can that be? What else absorbs the energy when they jump from greater heights? (Hint: How did the person in part (a) land? How do people normally land when they jump from greater heights?) (c) Why might older people be much more prone than younger ones to bone fractures from simple falls (such as a fall in the shower)?

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QUESTION:

Problem 10E

BIO Bone Fractures. The maximum energy that a bone can absorb without breaking depends on characteristics such as its cross-sectional area and elasticity. For healthy human leg bones of approximately 6.0 cm2 cross-sectional area, this energy has been experimentally measured to be about 200 J. (a) From approximately what maximum height could a 60-kg person jump and land rigidly upright on both feet without breaking his legs? (b) You are probably surprised at how small the answer to part (a) is. People obviously jump from much greater heights without breaking their legs. How can that be? What else absorbs the energy when they jump from greater heights? (Hint: How did the person in part (a) land? How do people normally land when they jump from greater heights?) (c) Why might older people be much more prone than younger ones to bone fractures from simple falls (such as a fall in the shower)?

ANSWER:

Solution 10E

Step 1:

Data given

Mass $m\ =\ 60\ kg\$

Area of cross section $A=\ 6.0\ c{m}^{2}$

Energy $W=\ 200\ J\$

$W=KE=\ PE=\ mgh\$

$200J\times{}2\ =\ 400\ J\$

$400\ J\$ is the energy used for both legs

$400\ J\ =\ mgh\$

$400\ J\ =60\ kg\ \times{}9.8\ m/{s}^{2}\times{}h$

$h\ =\ \frac{400\ J\ }{60\ kg\ \times{}9.8\ m/{s}^{2}}$

$h\ =\ 0.680\ m\$

From this we can note that the person has to jump from $\ 0.680\ m$ to stand upright without breaking any bone

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