The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that a leg bone of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing.

Verified step by step guidance

1. Identify the type of energy involved when the person lands. In this case, the potential energy (PE) at the maximum height is converted entirely into the energy absorbed by the bones upon landing.
2. Use the formula for potential energy, PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height in meters.
3. Set the potential energy equal to the maximum energy the bones can absorb without breaking, which is given as 200 J. So, set up the equation mgh = 200 J.
4. Substitute the mass of the person (60 kg) and the acceleration due to gravity into the equation, and solve for h, the height.
5. Rearrange the equation to isolate h and solve for h to find the maximum height from which the person can jump without breaking their bones.

Key Concepts

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height above the ground. In this context, it helps determine how high a person can jump before the energy from the fall exceeds the bone's energy absorption limit.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the kinetic energy gained during the fall converts into gravitational potential energy at the peak of the jump. Understanding this principle is crucial for calculating the maximum height a person can jump without exceeding the energy absorption capacity of their bones.

Impact Force and Rigid Landing

Impact force refers to the force exerted when an object comes to a sudden stop, such as when landing from a jump. A rigid landing implies that the legs do not bend upon impact, meaning all the kinetic energy is transferred to the bones. This concept is essential for understanding how the energy absorbed by the bones during landing relates to the maximum height from which a person can safely fall without injury.