Gravitational potential energy and conservative forces
What's a conservative force? Conservative forces are any force wherein the work done by that force on an object only depends on the initial and final positions of the object. In other words, the work done by a conservative force on a mass does not depend on the path taken by that mass. If the work done by a force follows this rule, then we call it a conservative force. For instance, the gravitational force on a 5 kilogram mass is 49 newtons. If the mass moves downwards by an amount of 6 meters, the work done by gravity is going to be 294 joules. Now let's start over. Say the mass again moves down 6 meters. But then it moves up 6 meters, then down again 6 meters. The work done by gravity for the first downwards trip was 294 joules. Then for the upwards trip, since the gravitational force is pointing in the opposite direction of the motion of the mass, the work done by gravity is going to be negative 294 joules. Then for the last trip downwards, the work again is positive 294 joules. That means that the total work done on the mass from gravity is still 294 joules, just like it was when the mass was lowered only once. In other words, the work done by the gravitational force doesn't depend on the specifics of the path taken by the mass. The work done by gravity only depends on the initial and final position of the mass. In fact, you could allow the mass to take any path from this initial point to the final point, and the work done by gravity is still just going to be 294 joules. Because the work done by gravity doesn't depend on the path taken, we call gravity a conservative force. The force exerted by a spring is another example of a conservative force. The total work done on a mass by a spring does not depend on the path taken by the mass. It only depends on the initial and final positions of the mass. The term conservative comes from the fact that conservative forces conserve mechanical energy, whereas non-conservative forces do not conserve mechanical energy. Mechanical energy is kinetic energy and potential energy. An example of a non-conservative force is friction. If I move a mass along a table from point A to point B, friction does a certain amount of negative work on the mass, which creates some thermal energy. If instead of going straight from A to B, I make the block go from A to B back to A over and over again, the work done by friction will become larger and larger. And it'll generate more and more thermal energy. Because the work done by friction depends on the path taken, friction is not a conservative force. Similarly, air resistance is not a conservative force since the work done by air resistance depends on the specifics of the path taken. It's useful to note that if a force is conservative, you could define a potential energy for that force. That's why conservative forces like gravity and spring forces have potential energies associated with them. And non-conservative forces like friction do not have potential energy associated with them. This makes sense because if you do work against the gravitational force by lifting a mass in the air, you can get that energy back out by letting the mass fall down, turning potential energy into kinetic energy. Similarly, if you do work against the spring force by compressing a spring, you can get that energy back out by letting the spring decompress, which turns the stored potential energy into kinetic energy. But if you do work against the force of friction, you'll have a hard time trying to get that energy back out. The energy's been dissipated into the form of thermal energy and is now randomly distributed along the ground and into the block.
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