# Conservative force?

1. Mar 14, 2015

### johann1301

If F is a force acting on a atom and is dependent on the velocity of the atom. Is the force conservative?

2. Mar 14, 2015

### jbriggs444

What do you think -- what is the definition of a conservative force?

3. Mar 14, 2015

### gleem

Velocity dependent forces are generally not conservative and exception is the Lorentz force due to a magnetic field acting on a charged particle although some would strictly speaking not consider this force conservative either.

4. Mar 14, 2015

### johann1301

Lets say

F=-av

If i integrate this, isnt it soley dependent on the start and end point? And thus, its conservative..?

5. Mar 14, 2015

### johann1301

a is just a constant.

6. Mar 14, 2015

### gleem

V is dependent of time since v = a*t = m*a. Isn't it clear therefore that the work in reaching a specific position will depend on the path traveled. The longer the path the more time and thus more work.

7. Mar 14, 2015

### gleem

my a is the acceleration due to the force

8. Mar 15, 2015

### Staff: Mentor

Certainly not. Consider $a=-1 \; N/(m/s)$ and an object which goes out a distance of 1 m at 1 m/s and then back at 1 m/s and another which goes out the same 1 m distance at 1 m/s and then back at 10 m/s. The force does 2 J of work for the first path and 11 J of work for the second. Furthermore, the work is non-zero, so both differ from the path which just stays at the endpoints.

9. Mar 15, 2015

### DrStupid

... or any other force always acting perpendicular to velocity (e.g. coriolis force).

10. Mar 15, 2015

### audire

Are you asking if force is always conserved? From my understanding yes f=mv thus it will always equation out to your mass and velocity on the other side of the equals sign?

11. Mar 15, 2015

### jbriggs444

That is not at all what is being asked.

A force is "conservative" if the work done on an object by that force as it moves along any path that loops back to where it started is always equal to zero. Note that in this context we are talking about a force "field" as in http://en.wikipedia.org/wiki/Field_(physics)