Question

How can you define a body’s total energy in terms of its mass, velocity and height from the ground (gravitational potential, kinetic and rest)?

Answer 1

The total energy of a body can be defined in terms of its mass, velocity, and height from the ground by considering the three main forms of energy involved: gravitational potential energy, kinetic energy, and rest energy (mass-energy equivalence).

1. Gravitational Potential Energy (PE): The gravitational potential energy of an object at a certain height above the ground is given by the formula: $PE=m\cdot g\cdot h$ where:

• $PE$ is the gravitational potential energy,
• $m$ is the mass of the object,
• $g$ is the acceleration due to gravity (approximately 9.8 m/s² on Earth),
• $h$ is the height of the object from the reference point (usually the ground).

2. Kinetic Energy (KE): The kinetic energy of an object in motion is given by the formula: $KE=\frac{1}{2}\cdot m\cdot v^2$ where:

• $KE$ is the kinetic energy,
• $m$ is the mass of the object,
• $v$ is the velocity of the object.

3. Rest Energy (mass-energy equivalence): According to Einstein's mass-energy equivalence principle (E = mc²), the rest energy of an object is given by the formula: $E=m\cdot c^2$ where:

• $E$ is the rest energy,
• $m$ is the mass of the object,
• $c$ is the speed of light in a vacuum (approximately $3\times$