Final answer:
The potential energy of the system increases when a bucket full of sand is lifted 20 ft. According to Bernoulli's equation, if the pressure is constant and kinetic energy per unit volume increases, the potential energy per unit volume of the fluid decreases.
Step-by-step explanation:
Regarding the student's question about the leaking bucket full of sand being lifted 20 ft, the correct statement is that (B) The potential energy of the system increases as the bucket is lifted higher off the ground. The weight of the sand does not change due to the bucket being lifted (A is incorrect). Also, the kinetic energy of the system (C) would only increase if the bucket is being moved faster, which is not stated in the problem. The leakage rate (D) could change due to various factors, but this is not certain from the given information.
With respect to Bernoulli's equation and fluid dynamics, if the pressure remains constant and the kinetic energy per unit volume increases, then (A) The potential energy per unit volume of the fluid decreases. This is due to the conservation of energy principle where the total mechanical energy of the system remains constant if there is no energy loss. Therefore, any increase in kinetic energy must be accompanied by a corresponding decrease in potential energy.