Work and Energy - Mission WE9 Detailed Help

A roller coaster car is nearing the end of the track and approaching the loading dock. It possesses 300 000 Joules of kinetic energy and 50 000 Joules of potential energy. A resistive force of 10 000 Newtons is applied to the car over a distance of 25 meters along a level section of the track. The new kinetic energy of the roller coaster car is ____ 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 roller coaster car slowing down, there is an applied force doing work upon it. The applied force is a non-conservative force and serves to change the total mechanical energy of the object. The amount of work done can be calculated (see Formula Frenzy section). Being a resistive force, the work will remove mechanical energy from the object. There will be an overall loss in energy - either due to a loss of kinetic energy, potential energy or both. The track is said to be level, so there is no loss in potential energy. The work done must be equal to the loss in kinetic energy. The final kinetic energy can be determined from the work done and the initial kinetic energy value.