The law of conservation of energy

[Quark]

The law of conservation of energy: Energy cannot be created nor destroyed, but merely transferred from one form to another. Why, then, does our moon continue to stay in orbit? - Earth's gravitational force. Indeed; however, this requires a tremendous amount of energy to do so, and has continued for billions of years. We know how it occurs, but why is this source of energy inexpendable? Does this not violate the law of conservation of energy, i.e. energy for free? And so too for magnets that continue to repel each other indefinitely with no identifiable energy source. Yet, the hands that endeavour to hold these two magnets together eventually weaken due to energy expenditure. This violates the aforementioned law; the magnets are drawing from an unknown bottomless energy source. How can this be?

[Xei]

I don't mean this in a patronising manner because you don't sound like a stupid person, but your knowledge of physics is very poor. If you want to really understand the answers you need to self-study a bit. The crux of your problem is that you have FORCE confused with ENERGY. The definition of 'work' is: Force applied x Distance moved in direction of force When something orbits, this does not require energy, because the force is being applied at right angles to the motion, and so there is 0 force in the direction of travel, and so 0 energy required. It is essentially the same situation with regards to energy as a mass moving through space in a straight line at the same speed. It doesn't require any energy; it just keeps going forever. Think also about whirling a conker on a string around your head. The tension force in the string causes the circular motion; the only reason you have to put a little bit of energy in to keep it going (using the chemical energy in the muscles in your hands) is that the frictional force due to air resistance acts against the conker in the direction of motion, hence work is done (i.e. energy is lost) - it is converted to heat energy of the air. Now, about magnetic fields: what fields do is create a force acting on a body. If these bodies move in the direction of the force, there is an energy change (for example, if you do work on a mass by applying an overall upward force to it on Earth hence lifting it into the air, you lose energy, and it gains energy; if you let the mass fall, the gravitational force instead does work on the mass, and it loses its potential energy, but gains kinetic energy). The only way that a magnet can cause energy changes is if you try and push the magnet into the field (in which case it gains magnetic potential energy) or let the magnet be pushed (it gains kinetic); if the magnet doesn't move, there is no energy change. It simply takes energy to hold your arm up because you are not truly letting the magnet rest in equilibrium; hence you are holding the magnet up, and also the whole mass of your arm, which of course requires your muscles to do work).

[Quark]

I'm genuinely interested. So, I'm assuming the work equation also corresponds to the amount of energy expended. The gravitational force of the earth holds objects down. According to the work equation, because the objects are stationary (d = 0), no work is done, and therefore no energy expended. However, if I attempted to move a large iron block but to no avail, then the work equation would calculate that I did no work, and thereby expended no energy - evidently, this is far from true. Both examples share similar application of the work equation. How would this be explained? With your conker example, are you suggesting that if I whirled a lead ball around on some string that it would expend no more energy than if I whirled a paper ball of similar proportions? How might this differ if the string was a spring - would we not arrive at an entirely different universal law of gravitation (The centripetal force equation would be different for a string-conker and a spring-conker)? Lastly, the 'modified work equation' uses the cosine of the angle that an object has moved relative to the force. So, if the object travels 90 degrees to the force then the equation calculates that no work was done, and no energy expended. Thus, orbiting objects are free from explaining energy use. But this ignores the fact that the object was already travelling past the planet irrespective of gravitational force, and that it is largely attributable to the downward pull of gravity that keeps the object moving in a circular motion.

[Xei]

Yes, 'work done' is roughly interchangable with 'energy used'. Energy is formally defined as the ability to do work - there is a one to one correspondence. You expend energy when trying to push something which you cannot because mantaining tension in the muscles is achieved via constant expenditure of chemical energy. The energy of the iron block does not change. Regarding the balls on strings; it would take more energy to get the iron ball to get up to a certain speed in the first place because you are the one which provides it with all of its kinetic energy = 1/2 m v^2 (hence proportional to mass); but after that, neglecting air resistance, no more energy is needed to keep either of the balls moving. You might as well attatch the string to a pole stuck in the ground - an object clearly not capable of doing any work - and you would achieve the same result as holding it. The paper ball would in reality stop faster because it has less kinetic energy in the first place and also probably has a higher coefficient of friction with the air so it does work against the greater resistive force at a greater rate. I'm not sure how the results would be any different for a spring.

[Quark]

You expend energy when trying to push something which you cannot because mantaining tension in the muscles is achieved via constant expenditure of chemical energy. The energy of the iron block does not change. Indeed, I'm not questioning the method of energy expenditure, but the fact that energy is expended. And yet, the work done, and thereby energy expended, would equal zero according to the equation. This is a nonsensical application of the work application, but the same logic is used to justify the force of gravity on objects that remain stationary on earth. Is it not?

[Xei]

You have to be careful, the applications of the equation can be extremely subtle; in your example, work is being done via chemical changes in the muscles, because chemical changes involve the movement of electrons through electrostatic fields. That explains why 'you' lose energy. Looking instead at the block: there is the force that you are applying acting on it in the forwards direction. However there is also a frictional force due to the floor acting in the opposite direction. Therefore the total force is 0, the block does not move, and no work is done on the block. Stationary objects on Earth do not experience energy changes for the same reason: the downwards force of gravitation is exactly balanced by the upwards force due to electrostatic repulsions between the electrons which surround the atoms which make up the object and the ground, hence 0 total force, 0 motion, and 0 work done.

[Quark]

Ahh ok, that appears to explain that. Now, that conker and string example has assumed equivalence to how planets orbit the earth, right? The centripetal force equation assumes so. However, no matter how fast one swings a ball on a string its orbital distance remains the same. The only way that this could be true for orbiting planets is if the gravitational force increased to compensate for the increase in velocity. In reality, if an orbiting planet is given more thrust then it's distance to the locus of gravity increases. In other words, a spring and conker would be more physically equivalent as the same occurs with an increase in velocity. The equations must differ for these effects? That's my last question. You shall bring rest to my chaotic mind.

[Xei]

The situations would be quite different, because the tension in a spring increases proportional to the extension, wheras the gravitational force decreases in a relationship where the force is proportional to the inverse of the square of the separation of the bodies. You can derive it all from the formulae F = mv^2 / r For centripetal acceleration, F = kx For a spring, and F = GMm/r^2 For the gravitational force. This all becomes pretty basic if you do A-Level physics (assuming you're still in school).