Work and Energy - Mission WE9 Detailed Help

A 1000-kg car moving with a speed of 20 m/s is approaching a stop light. The light turns yellow and the car makes an abrupt stop over a distance of 24 meters. The amount of mechanical energy that is converted to heat and other non-mechanical forms is approximately ____ Joules.

Work - Mechanical Energy Relationships:
If non-conservative forces do net work upon an object, then the total mechanical energy of that object is changed. The sum of the kinetic and potential energies will change as work is done upon the object. The amount of work done on the object by non-conservative forces is equal to the amount of change in mechanical energy.

Mathematically, work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d) that the force causes, and the angle (Θ) between the force and displacement vectors. The formula is       
W = F • d • cosine(Θ).

In the case of the car slowing to a stop, there is a resistive force (such as friction) doing work upon it. The friction force is a non-conservative force and serves to change the total mechanical energy of the car (see Know the Law section). The kinetic energy of the car will be changed into non-mechanical forms of energy such as heat and sound. The overall change in mechanical energy will be equal to the amount of non-mechanical energy that is produced. The original kinetic energy of the car can be calculated (see Formula Frenzy section). The final kinetic energy of the car is 0 Joule. The loss of kinetic energy is equal to the gain in non-mechanical forms of energy.