Final answer:
The work done by a roller coaster car halfway down a hill is the decrease in its potential energy, which is 6,000 joules. This is option (a) and complies with the conservation of energy principle.
Step-by-step explanation:
The question is about the work done by a roller coaster car as it moves halfway down a hill. Initially, the car has 10,000 joules of potential energy at the peak. As it descends halfway down the hill, this potential energy decreases to 4,000 joules.
According to the law of conservation of energy, in the absence of significant energy losses due to factors such as friction or air resistance, the car's total mechanical energy remains constant. Therefore, the loss of potential energy translates directly into an equivalent amount of kinetic energy. This transformation between energy types is governed by the work-energy theorem, which states that work done by the car is equal to the change in kinetic energy.
Calculate the work done by finding the difference in potential energy at the two points, which is:
Work done = Initial potential energy - Final potential energy
Work done = 10,000 J - 4,000 J
Work done = 6,000 J
Thus, the correct answer is (a) 6,000 joules. This amount of work was done on the car due to gravity alone, which performed positive work as the car descended half way down the hill, converting potential energy to kinetic energy.