Question

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See Figure 7.34.)

Figure 7.34 A car experiencing non-negligible friction coasts down a hill, over a small crest, then downhill again, and comes to a stop at a gas station.

Short answer

When the car coasts down the hill, its potential energy gets converted into kinetic energy and when it coasts up over the crest, its kinetic energy gets converted into potential energy. In the presence of friction, the total energy of the car decreases throughout the ride.

Step-by-step solution

Mechanical energy

When a nonconservative force acts on the body, the work done by all nonconservative force will add to the mechanical energy.

Conversion of energy

When the car coasts down the hill, its potential energy gets converted into kinetic energy and the car accelerates, hence its speed increases.

Since, the car descends down the hill in the presence of friction, its total energy decreases.

When the car coasts up over crest, its kinetic energy gets converted into potential energy and its speed decreases.

Again, when the car descends down the hill, its potential energy gets transformed into kinetic energy.

When the driver applies the breaks to stop, the friction force of the breaks converts the kinetic energy of the car into the thermal energy which is dissipated into atmosphere