The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that a leg bone of a healthy, 80 kg
human can absorb about 220 J
.
Part A
From what maximum height could a 80  kg
person jump and land rigidly upright on both feet without breaking their legs? Assume that all energy is absorbed by the leg bones in a rigid landing.
Express your answer with the appropriate units.
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h
=

To find the maximum height from which a person could jump and land without breaking their legs, we'll use the concept of energy conservation. The gravitational potential energy at the height \( h \) is converted into kinetic energy just before impact, and this kinetic energy is then absorbed by the legs.

Given dataTo find the maximum height from which a person could jump and land without breaking their legs, we'll use the concept of energy conservation. The gravitational potential energy at the height \( h \) is converted into kinetic energy just before impact, and this kinetic energy is then absorbed by the legs.

Given 
- Mass \( m = 80 \, \text{kg} \)
- Maximum energy the legs can absorb \( E_{\text{max}} = 220 \, \text{J} \)
- Gravitational acceleration \( g = 9.81 \, \text{m/s}^2 \)

The potential energy at height \( h \) is given by:
\[
E_{\text{potential}} = mgh
\]

This energy must be equal to the maximum energy that the legs can absorb:
\[
mgh = 220 \, \text{J}
\]

Now, solving for height \( h \):
\[
h = \frac{220 \, \text{J}}{mg}
\]

Substitute the values:
\[
h = \frac{220 \, \text{J}}{80 \, \text{kg} \times 9.81 \, \text{m/s}^2}
\]
\[
h \approx \frac{220}{784.8} \, \text{m}
\]
\[
h \approx 0.28 \, \text{m}
\]

Thus, the maximum height \( h \) from which the person can jump without breaking their legs is approximately **0.28 meters**.

Do you have any questions or would you like further details on this calculation? 

Here are five related questions to expand on this topic:
1. How does the height change if the person's mass increases?
2. What happens to the maximum height if the energy absorption capacity of the bones increases?
3. How would you calculate the height if the landing wasn't rigid?
4. What other factors could affect the amount of energy absorbed by the bones?
5. How would air resistance affect the calculated height?

**Tip:** Always consider the energy absorption capacity of materials when designing structures or evaluating physical activities to avoid injuries.

Learn how to calculate the maximum height from which an 80 kg person can jump and land rigidly upright without breaking their legs. This problem involves using energy conservation principles and specific data points such as mass, maximum energy absorption of leg bones, and gravitational acceleration.

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