Why is the work of a constant force conservative?

[AntoineCompagnie]

Homework Statement

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?

Homework Equations

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.

 

[Dr. Courtney]

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

 

[ehild]

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

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

 

[Dr. Courtney]

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

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.

 

[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.

 

[ehild]

Homework Statement

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?

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).

 

[Sonal]

The workdone by a conservative force is independent of path. We find the work done by doing a line integral for all kind of force. So to check just take any constant force like ai + b j and integrate that with dl along any curve you want. You will see that you don't have to put the information of curve while solving the integration. Just the end points will solve it.
So mathematics tells that constant force doesn't depend on path.
And constant force means it doesn't depend on X,Y,Z