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It's been a few years since my physics classes, and I want to do a quick double check to make sure I correctly remember the fundamentals of mechanical work.

1) At the most basic level, work is a force applied to an object, across a distance (that is, work cannot be calculated where there is no motion), yes? In the simplest case, where an object is experiencing linear motion, and the direction of force is either in the exact same direction, or the exact opposite direction, this corresponds to the formula:

Work = Force * distance, where work, force, and distance are simple scalar values (not vectors).

If you need to get fancier, you can use vectors (either 2D or 3D), with corresponding formulas which basically are the same thing, but take into account the direction of the force, versus the direction of the motion (only the fractional component of the force which is in the same or opposite direction as the motion is multiplied by the scalar of the distance, to produce work; this can be done using either trigonometry with angels, or with vector products [dot-product or cross-product, don't remember right now, but I can look it up later])?

2) In a system where multiple forces are acting upon an object, we can calculate the individual work of each force, and also a "net work", which is the work accomplished by the "net force", which is the sum of all forces.

So, for example, a person in a small boat with an outboard motor, going upstream in a river (assuming a 'simple' current model where there's no eddies, etc, but all of the force of the current is in the same direction, downstream). The motor produces a force upon the boat, in the upstream direction. The current produces a force on the boat in the downstream direction. For the boat to move upstream, the force of the motor must be greater than the force of the stream.

If the boat moves 10 meters upstream, we can say that the motor did 10F_motor Joules of work (in this case, not taking the net force into account)? Is that a valid statement? Or does "work" only apply to F_net * distance? I think we can also say that the stream did 10F_stream joules of negative work on the boat? Together, the Net work = 10 (F_motor - F_stream)?

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# Review of mechanical work

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