The force on a particle, acting along the x axis, varies as shown in Fig. 6–38. Determine the work done by this force to move the particle along the x axis:

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The work done by a force that changes in strength is the area underneath the force displacement curve. So between zero and ten seconds, we have this area here which we can break up into three pieces; A 1 has this triangle, A 2 is this rectangle and A 3 is this triangle. So find the area of each, add them together and that's the total work done. So we have one-half times the base of this triangle, which is 3 times its height of 400, and then plus, looks like it's about 4 units from 3 to 7 here for this width of this A 2 rectangle times 400 its height and then plus one-half times 3, which is the base, times 400 for A 3. That gives a total of 2800 joules of work done. For part (b), the work done from 0 to 15 is this total work done here, that we just calculated; subtract this work done because the force and the displacement are in negative directions; the force is negative here. So, we have A 4 as this little triangle, A 5 as this rectangle and A 6 as this little triangle. And it looks like A 4 has a a base of about one and a half meters and divide that by two times by 200, its y-coordinate, negative 200. And then minus 2 times 200, which is the rectangle A 5 and then minus one and a half times 200 over 2 for a total work of 2100 joules of between 0 and 15 seconds.