Line+Integral+2

=Line Integral of Work Type - Calculate Work of Vector Field F along Curve C.= This interactive approximates the work done by a 2d vector field F along a curve (oriented in the positive x direction).

Directions
 * Enter Fx=x-component and Fy=y-component of your vector field F in the input fields ( Fx=P and Fy=Q ).
 * Change xn=Number of x Steps and the endpoints xmin and xmax of your curve
 * Change v=vectorScale (readability)
 * Enter a different function f(x) for the curve (explicit in x),

media type="custom" key="12516426"

The interactive is to help us understand the principles behind the line integral for work (often called type 2). From Physics 1, we know that work is force*distance, e.g. if we push a box with F=3N for 5m, we have done work: W=15Nm This is easy to understand for a constant force directly along the path of a straight line. But: What if the path is a curve C? What if the force F is a vector function - this means both its direction and magnitude change with its position in space. How then do we measure the work done by F along C?

Additional changes can be made to yn=Number of y Steps as well as ymins and ymax and vh=VectorHead (readability).

Mathematics, Sage 3d Pages and Videos

References:
 * 1) [|Formula Sheet]
 * 2) [] (referenced 28.01.2012)