What are the Basics of the Work System in Physics?

[physic2hard]

First off i want to say thank god i found a board dedicated to helping out with physics, i am having so much trouble with this subject, and ironically, I am pretty good in math. well anyways i wasnt to sure about posting here or in the homework/class section, but since i just need to know the basics and not any help on my work, i decided here.
so to start off, can someone who has the patience and time just give me the basics about the work system(totally made the name up, when i say that i mean the potential and kinetic energy relations). i get the super basic ideas,such as ina conservative system, the total work in a system is always constant and i get the formulas such as U=mgy, but i feel I am missing some important key information to actually get the whole thing and how it works.
so if its not to much of a hassle or burden, can someone help me out here, thanks and I am sorry if this isn't something for the boards but more for the teacher at school to do, I am kinda new and desperate to get this stuff. oh and if this belongs on another board then just tell me and ill go there and close this one if i can

 

[TriTertButoxy]

Hi there! Welcome to the boards, physic2hard. I'd be glad to help, you; but unfortunately, I'm getting ready to go to bed. I'll try to post more tomorrow.

When I started out learning about phyiscs, I noticed that you can solve systems using two ways:

1. Write out a force diagram, and use Newton's F = ma to extract the equation of motion.

2. Study the system, and take note of the energies involved (ie kinetic and potential). Write out the law of conservation of energy (and that of momentum) and then extract the equation of motion from there.

Both methods are equivalent, althuogh one method is better that the other depending on the situation.

So let's pay attention to the second method, since that will obviously make extensive use your so called work system.

As you know, in nature, there are two normal kinds of 'energies': the kinetic energy, and the potential energy. While the kinetic energy for a particle can be quantified by

\text{KE}=\frac{1}{2}mv^2.​

For conservative forces (gravitational and electromagnetic forces), one can assign a 'potential energy' of a particle. For this reason, the potential energy for a given particle is system dependent. In most cases, the system is subjected to some uniform force field, like the graviational force at Earth's surface. In this particular case, the potential energy is given by

\text{PE}=mg\text{(height)}.​

Here, the height of the particle (or object) can be measured from anywhere - the ground, the surface of the table, or at the top of a building. However, once you've picked a reference height to measure the potential energy of the system, you must keep it consistent throughout the problem.

As you probably already know, both of these energies can be derived from the defenition of work:

W=\int\vec{F}\cdot\text{d}\vec{x}​

.

If you haven't already done so, I'd say it would be a rather good exercise for you to try to derive the expressions for the kinetic energy of a moving particle, and for the potential in a gravitational field. Having a good command of this idea, you can extend this principle to study non-conservative forces, like friction!

Anyway, time for bed . More tomorrow!

 

[physic2hard]

when you put it like that its pretty simple, i get the concept,but for some reason it complicates itself when it turns into say a block on a pulley, and you had to find the speed of the other block when block one falls, what do i do then, i might get it more better now tho, thanks to method 2 you put,by identifying the forces acting on a block. thanks for the help and id appreciate anymore information you have to give, thanks