Final answer:
The work required to stretch the spring from x=0 to x=3m is 63 Joules.
Step-by-step explanation:
To calculate the work required to stretch the spring from x=0 to x=3m, we need to find the potential energy difference between the two positions. The work done by a spring force is given by the equation W = − ∠ x2 F(x) dx, where F(x) is the force function. In this case, the force function is f(x) = 20x − x3 N. To find the work, we need to integrate the force function with respect to x from x = 0 to x = 3, which gives us:
W = ∠0>3 (20x − x3) dx
W = [10x2 − (1/4)x4] from 0 to 3
W = (10(3)2 − (1/4)(3)4) − (10(0)2 − (1/4)(0)4)
W = (90 − 27) − 0
W = 63
Therefore, the work required to stretch the spring from x=0 to x=3m is 63 Joules.