The maximum height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72-kg person in such a jump? Where does this energy come from?

Verified step by step guidance

1. Identify the initial and final positions of the jump. The initial position is at ground level, and the final position is at the maximum height of 60 cm (0.6 meters).
2. Use the formula for gravitational potential energy, which is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi> = <mi>m</mi><mi>g</mi><mi>h</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is the mass of the person (72 kg), <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is the acceleration due to gravity (approximately 9.8 m/s²), and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> is the height (0.6 meters).
3. Calculate the initial gravitational potential energy at ground level, which is zero since the height is zero.
4. Calculate the final gravitational potential energy at the maximum height using the formula: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi> = 72 imes 9.8 imes 0.6</mi></math>.
5. The increase in gravitational potential energy is the difference between the final and initial potential energies. This energy comes from the chemical energy stored in the muscles, which is converted into kinetic energy during the jump and then into potential energy at the peak of the jump.

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 a reference point. In this context, the increase in GPE is due to the person jumping to a height of 60 cm.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a jump, the chemical energy stored in the muscles is converted into kinetic energy as the person pushes off the ground, and then into gravitational potential energy at the peak of the jump.

Muscle Energy Conversion

Muscle energy conversion refers to the process by which muscles convert chemical energy, derived from nutrients, into mechanical energy. During a jump, this mechanical energy is used to propel the body upwards, overcoming gravitational forces. The efficiency of this conversion affects the height a person can achieve in a jump.