Lou’s latest invention, aimed at urban dog owners, is the X-R-Leash. It is made

Question

Lou’s latest invention, aimed at urban dog
owners, is the X-R-Leash. It is made of
a rubber-like material that exerts a force
Fx = (-7.3 N/m) x - (62 N/m2) x2 when it
is stretched a distance x. The ad claims,
“You’ll never go back to your old dog leash
after you’ve had the thrill of an X-R-Leash ex-
perience. And you’ll see a new look of respect
in the eyes of your proud pooch.”
Find the work done on a dog by the leash
if the person remains stationary, and the dog
bounds off, stretching the X-R-Leash from
x = 0 m to x = 21 m.
Answer in units of kJ.


please help

Explanation / Answer

dW = F dx = -(7.3 x + 62 x^2) dx x = -(7.3 x^2 / 2 + 62 x^3 / 3) x = -(1610 + 191400) = -193000 = -193 kJ

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