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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.
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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).
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In the case of the cart being pulled up the inclined plane, 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 (see Know the Law section). The amount of work done can be calculated (see Formula Frenzy section). Since the force is in the direction of the motion, positive work is done in order to add mechanical energy to the object. There will be an overall gain in energy - either due to a gain of kinetic energy, potential energy or both. The cart is said to be pulled at a constant speed, so there is no gain in kinetic energy. The work done on the cart must be equal to its gain in potential energy. The final potential energy can be determined from the work done and the initial potential energy value.
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