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).