people who r good at physics .. i need help please.. thanx..?

Question

conservation of energy..
v know P.E = MGH.....AND k.e = 1/2 MV*V..

U TAKE a body of mass M TO a height H IT GAINS a potential of MGH.....

SAY if u can prove MGH > 1/2MV*V....otherwise....P.E > K.E...and that some of potential energy is not recovered.....and hence violating law of conservation of energy. .. what effect will it have on current physics...?? r how central is L.C.E....??

THANX..N CHEERS..

Answer 1

In fact, this is a mathematical artefact! P.E has been built (or defined) in order to have conservation of energy.

Answer 2

Energy is a funny thing in that I can define the potential energy to be zero anywhere along the path from the ground to height H. There is nothing that requires me to have the PE be zero on the ground.

Now suppose you have a mass m on the ground and you lift it to a height H. The work done in lifting it is the integral of the force of gravity on the object over the vertical path it travelled - looks like SF dy where the "S" is an integral sign. F = mg and the integral runs from 0 to H. So the result is Work = mgH.

Now I did that much work, which means I expended energy. The energy was converted from kinetic (I had to move it up) to potential. Now, if I drop the object I recover that energy. Since it is falling vertically, I can show using kinematics (no energy invoked) :
h = (V^2 - V0^2)/(2*g) where V0 is the initial velocity and that is zero - the object starts from rest.

Hence, the mass is moving at a speed V= sqrt(2gh) and since KE is 1/2mv^2 one sees the KE = PE as it has to be.

If I define the mass as having zero potential energy at height H, then the work done is negative, the PE is negative and energy ios still conserved.

The only way to get more PE than KE is to stop the mass before it hits the ground, but then it still has some PE so the total energy is conserved.

Conservation of energy is a very powerful and fundamental law in physics and we have not seen it violated.

Answer 3

The conservation of energy is about as central to the science of physics as it gets. If this law toppled, it would turn the world of physics upside-down.

Regarding your conversion of potential energy into kinetic energy, some of that energy may be lost to friction, drag, etc., during the conversion. So if you see a discrepancy between PE and KE, start looking there.

Answer 4

In an experiment you will always find Ep>Ek because some of the Pe is lost to friction producing heat. If you would be able to do this experiment on the moon you would find that Ep=Ek.

Well almost, this Ek equation is in Newtonian science and is a fair approximation of the more precise (exact?) equation Einstein drew up: Ek=(m*c*c)/sqr(1-((v/c)*(v/c))-m*c*c
check the link for a better visual.