What does the area under a force vs. position curve represent?

[sisika]

Homework Statement

A small box is moved from position x1 to x2 by a net force which varies with position. On a graph, I plot the net force on the box vs. its position. The area in between the force curve and the x-axis is ...... And I am not sure if it is the work done on the box or may be something else

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

Homework Statement

A small box is moved from position x1 to x2 by a net force which varies with position. On a graph, I plot the net force on the box vs. its position. The area in between the force curve and the x-axis is ...... And I am not sure if it is the work done on the box or may be something else

The area enclosed by the curve and x-axis is indeed the net work done by the force. The formal definition of work;
$$\int^{x_1}_{x_0}f(x) dx$$

 

[m2003]

The area under the force vs. position curve represents the work done on the box. This is because work is defined as the product of force and displacement, and the area under a curve represents the product of the two variables. Therefore, the area under the force vs. position curve represents the total work done on the box as it is moved from position x1 to x2. This can be calculated by finding the integral of the force function over the interval from x1 to x2.