A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point)

Responses

Mass is eliminated when equating gravitational potential energy with kinetic energy.
Mass is eliminated when equating gravitational potential energy with kinetic energy.

Mass is eliminated when equating elastic potential energy with kinetic energy.
Mass is eliminated when equating elastic potential energy with kinetic energy.

The mass of the ball is insignificant compared with the mass of Earth.
The mass of the ball is insignificant compared with the mass of Earth.

The displacement of the ball is insignificant compared with Earth's size.

1 answer

The correct response is:

Mass is eliminated when equating gravitational potential energy with kinetic energy.

In the context of conservation of mechanical energy, gravitational potential energy (PE) and kinetic energy (KE) are given by the formulas:

  • Gravitational potential energy: \( PE = mgh \)
  • Kinetic energy: \( KE = \frac{1}{2} mv^2 \)

When you analyze the conservation of mechanical energy as the ball falls, you can set the initial potential energy equal to the kinetic energy just before it hits the ground:

\[ mgh = \frac{1}{2} mv^2 \]

In this equation, the mass (m) appears on both sides and can be canceled out, indicating that the analysis of energy conservation does not depend on the mass of the ball. Thus, the principle of conservation of mechanical energy is indeed independent of the mass of the object in this case.