Question
A student investigates the relationship between gravitational potential energy and kinetic energy by sliding a smooth ice cube along the inside of a large punch bowl. The diagram shows five positions of the cube in the bowl. At what position is the kinetic energy of the ice cube the GREATEST?
II
III
IV
v
II
III
IV
v
Answers
GPT-4o mini
To determine at which position the kinetic energy of the ice cube is greatest, we need to consider the concept of energy conservation in the system, particularly gravitational potential energy (GPE) and kinetic energy (KE).
Gravitational potential energy depends on the height of the object above a reference point. As the ice cube slides down from a higher position to a lower one, its gravitational potential energy decreases, and this energy is converted into kinetic energy. Therefore, the lower the position of the cube in the bowl, the more kinetic energy it will have, assuming no energy is lost to friction (since it's a smooth surface).
Let's analyze the provided positions:
- **Position II**: Higher than III, IV, and V. GPE is higher, KE is lower.
- **Position III**: Lower than II but higher than IV and V. GPE is reduced compared to II, resulting in some increase in KE.
- **Position IV**: Lower than III and II, GPE decreases further, and KE increases.
- **Position V**: The lowest position in the bowl. GPE is at its minimum, and consequently, KE is at its maximum.
Therefore, **Position V** is where the kinetic energy of the ice cube is the GREATEST, as it has converted the maximum amount of gravitational potential energy into kinetic energy by reaching the lowest point in the bowl.
Gravitational potential energy depends on the height of the object above a reference point. As the ice cube slides down from a higher position to a lower one, its gravitational potential energy decreases, and this energy is converted into kinetic energy. Therefore, the lower the position of the cube in the bowl, the more kinetic energy it will have, assuming no energy is lost to friction (since it's a smooth surface).
Let's analyze the provided positions:
- **Position II**: Higher than III, IV, and V. GPE is higher, KE is lower.
- **Position III**: Lower than II but higher than IV and V. GPE is reduced compared to II, resulting in some increase in KE.
- **Position IV**: Lower than III and II, GPE decreases further, and KE increases.
- **Position V**: The lowest position in the bowl. GPE is at its minimum, and consequently, KE is at its maximum.
Therefore, **Position V** is where the kinetic energy of the ice cube is the GREATEST, as it has converted the maximum amount of gravitational potential energy into kinetic energy by reaching the lowest point in the bowl.