# Why does the work of a constant force is conservative?

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1. Jan 26, 2016

### AntoineCompagnie

1. The problem statement, all variables and given/known data

Why for a given constant force, in a study reference system, which point of application moves from A to B, the work of the force is conservative?

2. Relevant equations

3. The attempt at a solution
The only thing I know is that if the angle $(\vec{F},\vec{AB})$ is acute $W_{AB}$ is an engine work else, its resilient.

2. Jan 26, 2016

### Dr. Courtney

Some constant forces are not conservative, sliding friction, for example.

3. Jan 26, 2016

### ehild

Sliding friction is not a constant force. Its magnitude is constant but the direction is opposite to the velocity.

4. Jan 26, 2016

### Dr. Courtney

If the direction of the velocity is constant, then both the magnitude and direction of the sliding friction force vector are constant.

If the magnitude and direction of a vector are constant, then the vector is constant. Yet, friction is not conservative.

Another example is the drag force on a falling object that has reached terminal velocity in air. The drag force is constant, but it is not conservative.

5. Jan 26, 2016

### ehild

http://www.britannica.com/science/conservative-force

A function f(x) is not constant function, even in case x has a definite value. Friction depends on the direction of velocity. The work done between points A and B and back to B to A is not zero, because the velocity changes sign in the reverse path.

6. Jan 26, 2016

### ehild

The force is conservative, when the the work of the force does not depend on the path between points A and B. Along a closed path, the work is zero. In case of constant force, if the work is positive while the point of application moves from A to B, it is negative when moving back to B to A. Look at the angles between force and displacements (the blue and green vectors in the figure).