Chapter 5: Applications of Integration

Section 5.8: Work

Example 5.8.1

$$ A weight of 3 lbs is attached to a spring hung from a hook, and the spring stretches 5 inches. How much work is done if the spring is stretched a further 8 inches? (Assume the spring obeys Hooke's law.) $$ Solution Mathematical Solution $$ Since $F\=k x$, the spring constant is $k\=3\/5$, with units lbs/in. Hence, the work done while stretching the spring a further 8 inches is $W$ = ${\int }_5^{13}\left(3\/5\right)x \mathit{\ⅆ}x\=216\/5$ in-lbs.  $$ $$ Maple Solution $$ Determine the spring constant from the given data, then write the appropriate definite integral.   •  Expression palette: Definite-integral template •  Context Panel: Evaluate and Display Inline ${\int }_5^{13}\left(3\/5\right)x \mathit{\ⅆ}x$ = $\frac{216}{5}$$$ $$

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