Question

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

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.

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

This is because, when considering conservation of mechanical energy, the gravitational potential energy (U) and the kinetic energy (K) can be expressed as follows:

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

When you set these two equations equal to each other to express conservation of energy (i.e., potential energy converted into kinetic energy), the mass (m) appears in both terms and cancels out, showing that the conservation of energy does not depend on the mass of the object.