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. Calculate the gravitational potential energy (GPE) increase using the formula: GPE = mgh, where 'm' is the mass in kilograms, 'g' is the acceleration due to gravity (approximately 9.8 m/s^2), and 'h' is the height in meters.
2. Convert the jump height from centimeters to meters by dividing by 100, since 1 m = 100 cm.
3. Substitute the values into the formula: m = 72 kg, g = 9.8 m/s^2, and h (converted to meters).
4. Calculate the product of these values to find the increase in gravitational potential energy.
5. Understand that the energy comes from the muscular energy of the person. When the person jumps, the muscles do work against gravity, converting chemical energy in the muscles into kinetic energy and then into gravitational 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 the context of the jump, the increase in GPE corresponds to the height the person reaches during the jump.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the case of a jump, the kinetic energy generated during the crouched start is converted into gravitational potential energy as the person ascends. This transformation is crucial for understanding how the energy used in the jump is accounted for.

Kinetic Energy

Kinetic energy is the energy of an object in motion, defined by the formula KE = 1/2 mv², where m is mass and v is velocity. When a person crouches and then jumps, they convert muscular energy into kinetic energy, which propels them upward. This kinetic energy is what allows them to reach a certain height, and it is this energy that is transformed into gravitational potential energy at the peak of the jump.