![]() ![]() Let us first throw a ball and find the work done by gravity when the ball reaches the height (H).įor the next case, let us say we have thrown the same ball with a higher velocity such that, the ball passes the height (H), and travels further and reaches a height (L), and then comes back to (H) and finally reaches the ground. Let us now see what happens if we throw a ball in two different paths but with the same start and end points. ![]() We know that the gravitational force is given by the expression. Into the form of thermal energy and is now randomlyĭistributed along the ground and into the block.Proof- conservative forces are path independent The force of friction, you'll have a hard time trying Spring decompress, which turns the stored potentialĮnergy into kinetic energy. You can get that energy back out by letting the Similarly, if you do workĪgainst the spring force by compressing a spring, In the air, you can get that energy back outīy letting the mass fall down, turning potential energy And non-conservativeįorces like friction do not have potentialĮnergy associated with them. Like gravity and spring forces have potential energiesĪssociated with them. If a force is conservative, you could define a potentialĮnergy for that force. Is not a conservative force since the work doneīy air resistance depends on the specifics Taken, friction is not a conservative force. And it'll generate moreĪnd more thermal energy. Straight from A to B, I make the block go from A to Bīack to A over and over again, the work done by friction Table from point A to point B, friction does a certainĪmount of negative work on the mass, which creates An example of a non-conservativeįorce is friction. Mechanical energy is kineticĮnergy and potential energy. The term conservativeĬomes from the fact that conservative forcesĬonserve mechanical energy, whereas non-conservativeįorces do not conserve mechanical energy. On a mass by a spring does not depend on the Spring is another example of a conservative force. Taken, we call gravity a conservative force. The work done by gravity is still just going This initial point to the final point, and Gravity only depends on the initial and final In other words, the work doneīy the gravitational force doesn't depend on the specifics Joules, just like it was when the mass was That means that the total workĭone on the mass from gravity is still 294 Since the gravitational force is pointing in the opposite The work done by gravityįor the first downwards trip was 294 joules. If the mass moves downwardsīy an amount of 6 meters, the work done by gravity ![]() For instance, the gravitationalįorce on a 5 kilogram mass is 49 newtons. If the work done by aįorce follows this rule, then we call it aĬonservative force. In other words, the work done byĪ conservative force on a mass does not depend on the That force on an object only depends on the initial andįinal positions of the object. What's a conservative force? Conservative forces Most astronomers choose to say that if an object has enough KE to get free from a big gravitational object, then it has positive ME, but if it is trapped by the big object, then the negative PE is greater in magnitude than the positive KE, so the ME is negative. It has some KE, since it is moving in its orbit, but not enough to get free from the sun. Here is another very real-life example: the earth has negative mechanical energy, if you ask almost any astronomer! The reason is that the earth is "down in a hole" relative to the sun's gravitational pull. So to give you an example, if we are holding an object at y = 0 (say, ground level), and our friend is down in a hole (say, y = -10m), and we drop the object and he catches it and holds it at rest, then it has KE = 0 and PE = mgy < 0, so ME < 0. We just make the choice that we think will make calculations easiest. It can be the height where the object starts, where it finishes, the height of the ground level, or any other height. But the y = 0 height can be whatever you want. For example, we usually say that gravitational potential energy PEg = mgy, where y is the height of the object. In fact, PE is very often negative, but an extremely important fact about PE is that it is always up to YOU to decide what position is the PE = 0 position. KE is never negative, and it can only be 0 if the object is not moving.
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