# Work

My parents told me that a student’s job is to study, but where’s the money in that?

Oh, what’s that?
Blogging about the results of your exciting cyber exploits (after selling the software to the highest bidder heheheh >:D) might bring in the big bucks?

Instigating the masses with my invigorating insights into the realms of maths and physics might just reel in the cash cow from the proverbial cow pond? (These cows really enjoy a good soak every now and again. There’s a whole strategy to snag more than the other chumps along the bank and everything.)

So blogging? Worth it. My kind of work.

But Work in the physical sense isn’t that kind of work.

This kind of work is related to Force on objects; if the point of application of a force on a body moves, it’s said that work is done on that object – especially if the force is responsible for it.

Positive work is done when the displacement of the object is in the direction of the force applied, negative work is when it’s like the force is fighting a losing battle. For example, imagine you’re pushing a boulder up a hill. It’s pushing back, but if you’re making progress up the hill, then you’re doing positive work on the boulder. If you’re pushing with all your might, and it’s still going downhill in the opposite direction to the force you’re applying to it, then the work you’re doing is negative.

Otherwise known as “no good” work, or “not up-to-snuff” work. Here’s a mathematical description that should aide your intuition.

$\vec{W}=\vec{F}s$ , where s is the displacement in the direction of the force. In drawing up a Free Body Diagram, you first set up your coordinate axes, and if you define the direction your force is pointing in as positive, then of course, if the displacement happens to be in the reverse direction, then the sign on that lil s there is negative.

More generally, you can describe the displacement as a vector as well, and the general description of Work is the Dot Product of the force and the displacement: $\vec{W}=\vec{F}\cdot\vec{s}$ – but that’s equivalent to the first equation, as $\vec{W}=\vec{F}\cdot\vec{s}=|\vec{F}||\vec{s}|\cos(\theta) = \vec{F}s$

Go brush up on your Trigonometry if you don’t understand that.

Even more generally, the work done by a force on an object through a particular trajectory is defined using  an Indefinite Integral evaluated along that trajectory – but lil ol’ me doesn’t know how to type that up in LaTex quite yet (and it’s nearly time for my next lecture).

Any displacement in directions other than the direction of the force doing work doesn’t count, hence why the force of gravity does no work on orbiting bodies. Centripetal Acceleration is a funny thing.

In fact, with this example it’s plain to see the relationship between the work you’re doing to the system (the boulder), and the energy of the system – giving rise to what’s called the Work-Energy Theorem. It’s pretty alright, but that in itself is a contrived example (only works for Conservative Forces), so for now, be satisfied by the fact that you pushing the boulder up the hill is positive work, and conversely, you’re increasing the Gravitational Potential Energy, of the boulder system. Simple as dat.

The concept of work is actually pretty fundamental to the fields of Physics, as it’s related to Energy, and that’s used eeeeeeeeeverywhere.

Can you think of other examples of positive and negative work? It really shouldn’t be that hard, just remember the important things about it is the force and the displacement – another example that I’m pulling out my ass AT THIS VERY MOMENT is, like, imagine you were pushing on your phone that’s sitting on the table. It won’t move until you overcome the force of Static Friction. Till it starts moving, you ain’t doing any work on that bish.