BIO Bone Fractures.The maximum energy that a bone canabsorb without breaking depends on characteristics such as its $\mathbf{6}\mathbf{.}\mathbf{0}\mathit{c}{\mathit{m}}^{\mathbf{2}}$cross-sectional area and elasticity. For healthy human leg bones of approximately cross-sectional area, this energy has been experimentally measured to be about $\mathbf{200}\mathit{J}$. (a) From approximately what maximum height could a $\mathbf{\text{60 kg}}$ person jump and landrigidly upright on both feet without breaking his legs? (b) You areprobably 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)?

Gravitational potential energy is the energy an object possesses or gains as a result of a change in its position when it is present in a gravitational field. In simple terms, gravitational potential energy is the energy that is related to the gravitational force or gravity.

The gravitational potential energy is given as the product of the mass of gravity, and vertical displacements of the object.

$U_{\text{grav}}=mgh$ ….. (1)

Here, $m$ is the mass of an object, $g$is the is the gravitational acceleration, and $h$is the height of an object.

The energy of the two legs is,

$U_{\text{grav}}=2U$ ….. (2)

Here, the energy $U$is$200\text{J}$ .

Substitute the above values in the above equation.

$$\begin{gathered} U_{\text{grav}}=2\left(200\text{J}\right) \\ =400\text{J} \end{gathered}$$

Rearrange the equation (1) for $h$as follow.

$h=\frac{U_{\text{grav}}}{mg}$

Putting for $400\text{J}$, $U_{\text{grav}}$, $60\text{kg}$for $m$, and $9.8m/s^2$ for in the above equation, and you have

\(\begin{aligned}{}h = \frac{{400{\rm{ J}}}}{{\left( {60{\rm{ kg}}} \right)\left( {9.8{\rm{ }}{{\rm{m}} \mathord{\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}} \right)}}\\ = \frac{{400{\rm{ J}}\left( {\frac{{{{kg \cdot {m^2}} \mathord{\left/ {\vphantom {{kg \cdot {m^2}} {{s^2}}}} \right.} {{s^2}}}}}{{1{\rm{ J}}}}} \right)}}{{\left( {60{\rm{ kg}}} \right)\left( {9.8{\rm{ }}{{\rm{m}} \mathord{\left/ {\vphantom {{\rm{m}} {{{\rm{s}}^{\rm{2}}}}}} \right.} {{{\rm{s}}^{\rm{2}}}}}} \right)}}\\ = 0.68{\rm{ m}}\end{aligned}\)

Therefore, the maximum height that a parson can jump from and land upright with rigid legs without breaking them is $0.68m$ .

When people jump, they usually bend their legs when they land. In doing so, they cushion the landing by changing the angle between their leg bones and the force exerted on them by the ground. Using their muscles (and essentially their bodies) as springs slowly absorb the force of the impact.

Older people generally have less bone mass and bone elasticity than younger people. So their bones are less able to cope with mechanical stress. In addition to the old coordination difficulties. Thus, older people may not be able to use their bodies effectively in case of pillow shocks, as discussed in part (b). The bones of the elders may not be directly able to cope with the resulting stress in part (a) of the question.