ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?(1 point) Responses The displacement of the ball is insignificant compared with Earth's size. The displacement of the ball is insignificant compared with Earth's size. 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.

1 answer

The correct response is: Mass is eliminated when equating gravitational potential energy with kinetic energy.

When a ball falls, its gravitational potential energy (PE) is converted into kinetic energy (KE). The formulas for gravitational potential energy and kinetic energy are:

  • \( PE = mgh \) (where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height)
  • \( KE = \frac{1}{2}mv^2 \) (where \( m \) is mass and \( v \) is velocity)

When setting the initial gravitational potential energy equal to the kinetic energy at the point just before it hits the ground (ignoring air resistance), you have:

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

In this equation, the mass \( m \) appears on both sides and can be canceled out, showing that the conservation of mechanical energy does not depend on mass. Thus, the conservation of mechanical energy is independent of the mass of the ball.