What is a conservative force?

Question

What is the difference between a conservative and nonconservative force?

Answer 1

A conservative force is one which draws or supply no energy from or to a body in a complete round trip.

e.g When a body is thrown upward, its kinetic energy is decreased due to the downward pull of the earth. It reaches a definite height and then start to come down. During the downward trip, the downward pull of the earth supplies kinetic energy to the body. When it reaches the starting point the kinetic energy become same as its initial kinetic energy.

The potential energy of the body was zero initially, became maximum at the maximum height, and reduced to zero again.

Answer 2

Are you sure you don't mean a conservative field?  That's a field whose value only depends on where you are, not on which route you took to get there.

Answer 3

A conservative force is one that changes the potential energy by an amount that is independent of path. An example is gravity or a spring force

A nonconservative force changes the potential energy by an amount that is dependent on the path taken. An example is friction.

Answer 4

The line integral of a conservative force is path-independent, and depends only on the endpoints of the path.

If any two paths between the same two points will change the particle's kinetic energy by different amounts, the force is nonconservative.

So, for example: suppose you're in a space ship with rockets on the back, firing at a constant rate -- but you can control their direction a little, to turn and such. That's nonconservative, since there are many paths that could lead from point A in space to point B in space, some of them where you go very fast when you hit point B, some of them where you go very slow when you hit point B.

But gravity is a good example of a conservative force. Getting out of Earth's orbit requires a set amount of energy, period. You could launch sideways with that energy, though you'd go through a lot more of the earth's atmosphere (atmospheric drag is nonconservative), and, in principle, you'd still eventually leave Earth's orbit, just as you would if you launched straight up.