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# Conservative forces

A conservative force exists when the work done by that force on an object is independent of the object's path. Instead, the work done by a conservative force depends only on the end points of the motion. An example of a conservative force is gravity. Created by David SantoPietro.

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• when can the mechanical energy be negative(real life example)? •  Mech. E = KE + PE
KE is never negative, and it can only be 0 if the object is not moving.
PE, however can be negative. 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. For example, we usually say that gravitational potential energy PEg = mgy, where y is the height of the object. But the y = 0 height can be whatever you want. It can be the height where the object starts, where it finishes, the height of the ground level, or any other height. We just make the choice that we think will make calculations easiest. 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.

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. It has some KE, since it is moving in its orbit, but not enough to get free from the sun. 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.
• Right near the end of the video it is stated that the thermal energy is dissipated into the ground and into the block, but doesn't it also radiate into the surrounding air? • A problem in my physics book involves a mass hanging from a rope. It is pushed to the right by an applied variable force. It begins at rest and ends at rest. One of the parts of the question asks what is the work done by the tension in the rope. I reasoned that the work done by tension was a constant force and took the dot product of tension with the displacement of the mass to come up with an answer that it did some negative work on the mass. The answer in the book says that the work done was zero. Is this because it starts and ends at rest, or is it because the applied force is doing the work? • If the force is always perpendicular to the displacement, as is the case with rope tension and a hanging mass, then the work will be zero since work is the dot product of force and displacement. The work that was done is by you when you lift the mass before releasing it.
• can an object have PE and KE at the same time?
like a bird flying -does it possess PE or KE? • As explained above, we came to know that mass spring system is a conservative system, but wait, when the block attatched to the spring moves to and fro, it is also subjected to frictional force. So in this case it should be a non-conservative system rather than the conservative.
Why is it so that the mass spring system is a conservative system? • Why when you have friction, there will be thermal energy? • what is meant by Torque? • how can we know that a force is path dependent? • Having the force's equation, we can find it, but it is required to know how to find a function's curl. For example, if you calculate the curl of any force of the type F = f(r) --- (function of radius only), like gravity (k/r²), it will result in 0. Having curl equal to 0 will immediately imply that force field is conservative. If curl is not 0, the force field will not be conservative.  