The correct response is: Mass is eliminated when equating gravitational potential energy with kinetic energy.
When analyzing the conservation of mechanical energy in the context of gravitational potential energy (PE) and kinetic energy (KE), the formulas are:
- Gravitational Potential Energy: \( PE = mgh \)
- Kinetic Energy: \( KE = \frac{1}{2} mv^2 \)
In the calculation of the energy transformation as the ball falls, the mass \( m \) appears in both equations. When you set the potential energy equal to the kinetic energy (assuming no energy is lost to friction), you can rearrange the equation as follows:
\[ mgh = \frac{1}{2} mv^2 \]
If you divide both sides by \( m \) (assuming \( m \) is not zero), you get:
\[ gh = \frac{1}{2} v^2 \]
This shows that the relationship between gravitational potential energy and kinetic energy does not depend on the mass of the object. Therefore, the conservation of mechanical energy equation in this context is independent of mass.
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