In one case, a sports car, its engine running, is driven up a hill at a constant speed. In another case, a truck approaches a hill, and its driver turns off the engine at the bottom of the hill. The truck then coasts up the hill. Which vehicle is obeying the principle of conservation of mechanical energy? Ignore friction and air resistance.

Both vehicles are obeying the principle of conservation of mechanical energy.

Explanation:

Hi there!

The conservation of energy is always obeyed. Energy can't be generated or produced, it can only be transformed. Let's analyze the case of the truck first:

Initially, the truck has a given potential and kinetic energy. When the truck coast up the hill, with the engines off, the kinetic energy will diminish at the same rate at which the potential energy increases (because the height of the truck relative to the initial position increases). In other words, kinetic energy is being transformed into potential energy as the truck coasts up the hill. The gain of potential energy by the truck occurs at the expense of the kinetic energy.

In the case of the car, the potential energy increases while the kinetic energy remains constant (because the speed remains constant). The potential energy is not being generated at the expense of kinetic energy but at the expense of the chemical energy of the fuel. The car will have more kinetic energy than the truck at the top of the hill, but less chemical energy while the potential energy will be the same. The difference in the kinetic energy of the car and the truck will be equal to the difference in chemical energy.

In conclusion, the sum of the kinetic, chemical and potential energy of both vehicles will be the same at the top of the hill which means that conservation of energy applied to both vehicles.