## Exploration 6.6: Forces, Path Integrals, and Work

Fx(x,y) = | Fy(x,y) = N

Please wait for the animation to completely load.

Move your cursor into the animation, then click-drag the crosshair cursor with the mouse. The bar graph on the right displays the work done by the force along the path. For your reference, there are circles every 10 m that form a coordinate grid (position is given in meters and the result of the integral is given on the bar graph in joules). Use the "reset integral" button to re-zero the work calculation between paths. Restart.

For each force, answer the following questions:

1. Starting at the origin (the center, x = 0 m and y = 0 m) and moving to x = 0 m and y = 10 m, what is the work done by the force?
2. Starting at x = 0 m and y = 10 m and moving to x = 0 m and y = 0 m, what is the work done by the force?
3. Starting at the origin (the center, x = 0 m and y = 0 m) and moving to x = 0 m and y = -10 m, what is the work done by the force?
4. Starting at the origin (the center, x = 0 m and y = 0 m) and moving to x = 10 m and y = 0 m, what is the work done by the force?
5. Starting at the origin (the center, x = 0 m and y = 0 m) and moving to x = -10 m and y = 0 m, what is the work done by the force?
6. Starting at the origin (the center, x = 0 m and y = 0 m), choosing your own path around the animation and ending back at the origin, what is the work done by the force?

When you are through, feel free to experiment with forces of your own choosing.