Line Integral of Work Type - Calculate Work of F along Curve
- Linda Fahlberg-Stojanovska
- Differential Equation
This interactive approximates the work done by a 2d vector field F along a curve (oriented in the positive x direction). 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 for the curve (as an explicit function in x), ----- Additional changes can be made to yn=Number of y Steps as well as ymins and ymax and vh=VectorHead (readability).
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?