Questions: Does changing the mass change the amount of total energy? Why or why not?

Solution Steps

To determine whether changing the mass affects the total energy, we need to consider the basic energy formulas. The two primary forms of mechanical energy are kinetic energy and potential energy.

The formula for kinetic energy (\(KE\)) is given by: \[ KE = \frac{1}{2}mv^2 \] where \(m\) is the mass and \(v\) is the velocity. From this formula, it is clear that kinetic energy is directly proportional to the mass. Therefore, increasing the mass will increase the kinetic energy, assuming velocity remains constant.

The formula for gravitational potential energy (\(PE\)) is: \[ PE = mgh \] where \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height. Similar to kinetic energy, potential energy is also directly proportional to the mass. Thus, increasing the mass will increase the potential energy, assuming height remains constant.

Final Answer