Question

which of the following is the best explanation of the transformation of energy from x to y?
the coaster car has 100% potential energy at the x and as it goes to y the coaster car increases the kinetic energy because it is going fast. energy is not lost, but only transformed as the coaster car moves through the roller coaster.
at x the kinetic energy of the coaster car is at the highest and as it goes to y the kinetic energy is transforming into potential energy. energy is not lost, but only transformed as the coaster car moves through the roller coaster.
at x the coaster car is creating more energy because it is moving faster. as the coaster car moves to y some of that energy is destroyed as it slows down.
the coaster car has a lot of kinetic energy at x because it is going really fast. at the y point, the coaster car loses energy because it is slowing down.

Explanation:

According to the law of conservation of energy, energy is neither created nor destroyed but only transformed. At the highest point (assuming \(X\) is the highest point where the coaster car is momentarily at rest relative to vertical motion), the coaster car has maximum potential energy (\(PE = mgh\), where \(h\) is maximum). As it moves down (to \(Y\)), the height \(h\) decreases and the speed \(v\) increases. The potential energy is transformed into kinetic energy (\(KE=\frac{1}{2}mv^{2}\)). Energy is conserved in the process (neglecting non - conservative forces like air resistance and friction in an ideal case).

The first option is correct because:

• If \(X\) is the highest point (assuming no initial vertical velocity component at \(X\)), the coaster car has \(100\%\) potential energy (in an ideal case with no initial kinetic energy at \(X\)).
• As it moves to \(Y\) (lower height), its speed increases, so kinetic energy increases. Energy is transformed (potential to kinetic) and not lost.

The second option is wrong because if \(X\) is the highest point (assuming no initial velocity at \(X\)), kinetic energy at \(X\) is not the highest.

The third option is wrong because energy is not created. The law of conservation of energy states that energy cannot be created or destroyed.

The fourth option is wrong because energy is not lost (in an ideal case, and even in real - world cases with non - conservative forces, energy is transformed into other forms like heat due to friction, but not “lost” in the sense of disappearing).

Answer:

The first option: The coaster car has 100% potential energy at the \(X\) and as it goes to \(Y\) the coaster car increases the kinetic energy because it is going fast. Energy is not lost, but only transformed as the coaster car moves through the roller coaster.