A car of mass 987 kg is traveling on a horizontal segment...

A car of mass $987 \mathrm{~kg}$ is traveling on a horizontal segment of a freeway with a speed of 64.5 mph. Suddenly, the driver has to hit the brakes hard to try to avoid an accident up ahead. The car does not have an ABS (antilock braking system), and the wheels lock, causing the car to slide some distance before it is brought to a stop by the friction force between its tires and the road surface. The coefficient of kinetic friction is $0.301 .$ How much mechanical energy is lost to heat in this process?

Key Concepts

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to its change in kinetic energy. This principle is crucial in analyzing how the work done by friction (which is force times the distance over which it acts) results in the loss of mechanical energy, turning it into heat.

Unit Conversion

Unit conversion is the process of converting quantities from one unit system to another to maintain consistency in calculations. For example, the car's speed given in miles per hour must be converted to meters per second to correctly apply kinetic energy formulas in SI units.

Friction

Friction is the resistive force that opposes the relative motion between two surfaces in contact. In this scenario, kinetic friction (characterized by a coefficient of kinetic friction) converts the car’s kinetic energy into thermal energy during the sliding process.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is quantified by the equation KE = ½ mv², where m is the mass and v is the velocity. In this context, calculating the car’s kinetic energy helps determine the amount of mechanical energy that is converted into heat during braking.

Energy Dissipation

Energy dissipation refers to the transformation of energy from one form to another, often as a loss in useful mechanical energy. Here, the kinetic energy of the moving car is dissipated as heat due to friction when the brakes are applied.

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