At what point on a roller coaster is the gravitational potential energy ($\mathrm{GPE}$) the lowest?

• A. At the top of a loop
• B. At the highest point of the first hill
• C. At the midpoint between the highest and lowest points
• D. At the lowest point of the track, closest to the ground

Answer: (D)

Verified step by step guidance

1. Recall that gravitational potential energy (GPE) is given by the formula \(GPE = m \times g \times h\), where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity, and \(h\) is the height above a reference point.
2. Understand that GPE depends directly on the height \(h\): the higher the object is above the reference point, the greater its gravitational potential energy.
3. Identify the reference point for height, which is usually taken as the lowest point on the track or ground level, where \(h = 0\) and thus GPE is zero or minimal.
4. Compare the heights of different points on the roller coaster: the top of a loop, the highest hill, the midpoint, and the lowest point on the track.
5. Conclude that since GPE increases with height, the gravitational potential energy is lowest at the lowest point of the track, closest to the ground, where \(h\) is minimal.