A particle moves along a line at 45° to the x-axis as shown in the diagram. A force acts on the particle, given by
Find the work done on the particle as it moves from (0,0) to (2x0, 2x0).
Step I: Choose a coordinate system and model the system as a collection of differential elements:
The coordinate system is already given. We model the path as a collection of differential steps
Step II: Identify a typical element. Draw it on the diagram. Describe it using the coordinates.
A typical element is:
at coordinates x,y where y=x.
Step III: Express the contribution of this element to the desired sum in terms of the coordinates.
The contribution is the work
Step IV: Determine the limits of integration.
The limits are x=0 to x=2x0.
Step V: Evaluate the integral.