The correct response is:
Mass is eliminated when equating gravitational potential energy with kinetic energy.
In the conservation of mechanical energy, the potential energy (PE) and kinetic energy (KE) can be expressed as:
- Potential Energy: \( PE = mgh \) (where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height)
- Kinetic Energy: \( KE = \frac{1}{2}mv^2 \)
When analyzing the conservation of energy, you can set the potential energy at the top equal to the kinetic energy at the bottom (ignoring any air resistance):
\[ mgh = \frac{1}{2}mv^2 \]
When you rearrange this equation, you can divide both sides by \( m \), which cancels out the mass:
\[ gh = \frac{1}{2}v^2 \]
From this point, you can see that mass does not affect the relationship between gravitational potential energy and kinetic energy, thus demonstrating that the conservation of mechanical energy is independent of mass.
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