The conservation of energy, why does it work? Negative work vs positive work

[PhanthomJay]

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.

When a 10 kg object is 5 meters above the ground, it has a potential energy of 490 J with respect to the ground. When it falls to the ground, it has no potential energy with respect to the ground. The work done by gravity (that is,the earth) on the object is 490 J during this fall [- (0 - 490) = +490 J).

Energy is not work. Energy is the capacity to do work.

 

[Doc Al]

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.

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.)

But to say that potential energy 'has nothing to do' with force x displacement (I assume you meant force, not work) is not accurate. Gravitational potential energy does equal the work done against gravity.

 

[vkash]

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.)

this depends on your assumptions you can take g as positive but in that case many signs of other things also changed like velocity in downward direction which is usually taken as negative will positive.
Most of all taking g as +ve or -ve depends on assumptions in general we take it as -ve.

 

[SammyS]

...
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.)

I agree with Doc Al on this point, (and on all other points, as well as I can remember). In any Physics textbook with which I am familiar, the symbol 'g' stands for the magnitude of the acceleration due to gravity, as Doc Al said, so g is positive.

 

[PieOperator]

Just use netwons third law to connect the forces. Here's how to start... The force exerted onto object one from from object two is positive 10 Newtons. The force exerted onto object two by object one is negative 10 Newtons. Afterwards, connect the definition of work = force times displacement while making sure you keep in mind the laws of thermodynamics. It takes practice, but you will succeed oh grasshopper.