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vela
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It's notation for a path integral.
That's not correct.flyingpig said:Ok let me try this one more time, because i think I get it now and vector calculus isn't really needed here...
ΔKE = -ΔPE = Wab = Work done by other forces
The formula, by itself, isn't either one or the other. It's can be interpreted both ways.What is the most confusing thing here is terminologies.
½m(v² - v₀²) = -mg(h - h₀) <=== work done by gravity
Now here comes the problem, is that the formula for the work-energy theorem or is that the conservation of energy?
vela said:That's not correct
vela said:The formula, by itself, isn't either one or the other. It's can be interpreted both ways.
What you wrote, particularly with your comment, is a case of the work-energy theorem. All that theorem says is the change in kinetic energy of an object is equal to the work done on it by all forces. So if you're interpreting the RHS of the equation as the work done by gravity, you're obviously using the work-energy theorem.
You could interpret that same equation as ΔKE = -ΔPE, which would be an expression of the conservation of energy.
How you read the equation is up to you.
flyingpig said:Ok let me try this one more time, because i think I get it now and vector calculus isn't really needed here...
ΔKE = -ΔPE = Wab = Work done by other forces
vela said:That's not correct.
Just to reinforce what vela said, the work done by other forces, where by 'other' forces you mean forces other than conservative forces like gravity, That is, work done by other forces is the work done by non conservative forces, thenflyingpig said:What!? Oh man and here I thought i got it...
It looks like in this equation you are assuming only gravity forces act, in which case, using the conservation of mechanical energy principle,What is the most confusing thing here is terminologies.
½m(v² - v₀²) = -mg(h - h₀) <=== work done by gravity
Now here comes the problem, is that the formula for the work-energy theorem or is that the conservation of energy?
If you're asking if writingflyingpig said:What!? Oh man and here I thought i got it...
Isn't that what I had before?
Doc Al said:That mysterious red stuff--the mgh term--is called potential energy. It's the negative of the work done by gravity, which is why it's on the opposite side of the equation.
What did you have in mind?flyingpig said:-(-mgh)? Are there any other physical meaning to this?
Please explain what you mean as fully as you can. Give a specific example.flyingpig said:I am getting the feeling that mechanical energy is not the same thing as the work done by something.
That is right. It's the change in mechanical energy (the change in kinetic plus potential energies) that is the same as the work done by non-conservative forces. It's the change in gravitational potential energy that is equal to the negative of the work done by gravity. It's the change in kinetic energy that is equal to the work done by all forces.flyingpig said:I am getting the feeling that mechanical energy is not the same thing as the work done by something.
As PhanthomJay explained, mechanical energy is not the same as the work done by something. (Although sometimes you can use the work done by something to figure out the change in mechanical energy.)flyingpig said:As in like a definition. Like potential energy has nothing to do with work x displacement. It's just means how much energy something has at a certain height.
Doc Al said:No. As a mass is raised, the gravitational PE increases. (Gravitational PE is minus the work done by gravity. It's the work done against gravity.)
No, g stands for the magnitude of the acceleration due to gravity; it's always positive. (Taking down as negative, the acceleration due to gravity is -g.)
Doc Al said:...
No, g stands for the magnitude of the acceleration due to gravity; it's always positive. (Taking down as negative, the acceleration due to gravity is -g.)