Question

Stewart James, Calculus, Section 6.4, Page 449, Problem 5

Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work is done by the force in moving an object a distance of 8 m?

Can someone please help us with this question. The answer we keep getting does not match the answer displayed in the back of the book.

Thanks!

Answer 1

Er... graph?

Answer 2

Yeah man where's the graph???

Answer 3

Yeah, sorry about that. First time using this site. Importing the graph as we speak.

Answer 4

All right

Answer 5

We know:
\[
W=\int_CF\,dt
\]So, we simply compute the area under the graph, to receive:
\[
W=60+120=180\;\text{Joules}
\]

Answer 6

Since W = f x d, just find the area between the graph and the x-axis.

Answer 7

Thank you! That makes much more sense. I kept getting either 240 Joules or 120 Joules. Computing the area under the graph makes much more sense.

Answer 8

Sorry, an edit to my expression, which works in this case, but not in all:
\[
W=\int_CF\,d\mathbf{x}
\]And, sure thing...!