Question

a ball falls from a shelf. assuming there is no friction, why is the conservation of mechanical energy independent of mass? (1 point)
mass is eliminated when equating gravitational potential energy with kinetic energy.
the displacement of the ball is insignificant compared with earths size.
mass is eliminated when equating elastic potential energy with kinetic energy.
the mass of the ball is insignificant compared with the mass of earth.

Explanation:

When considering the conservation of mechanical energy for a falling ball (with no friction), the gravitational potential energy formula is \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height) and the kinetic energy formula is \(K=\frac{1}{2}mv^{2}\). By the conservation of mechanical energy \(mgh=\frac{1}{2}mv^{2}\). We can divide both sides of the equation by \(m\) (since \(m
eq0\)), which eliminates the mass. The other options are incorrect: displacement - Earth size comparison is irrelevant to energy - mass relation here; there's no elastic potential energy in this case (ball is falling, not on a spring); and ball - Earth mass comparison is not the reason for energy - mass independence in this energy - conservation equation.

Answer:

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