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SCALC$95\mathrm{.}4\mathrm{.}006.$

The table shows values of a force function $f(x),$ where $x$ is measured in meters and $f(x)$ in newtons.

$\backslash$table$[[x,5,9,13,17,21,25,29,33,37],[f(x),5,5\mathrm{.}5,7\mathrm{.}2,8\mathrm{.}7,9\mathrm{.}5,8\mathrm{.}4,6\mathrm{.}5,5\mathrm{.}4,4]]$

Use the midpoint rule with $n=4$ to estimate the work $W($in J$)$ done by the force in moving an object from $x=5$ to $x=37.$

w $$ J

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$5.[0/1$ Points$]$ SCALC$95\mathrm{.}4\mathrm{.}009.$

Suppose that $4$ J of work is needed to stretch a spring from its natural length of $28$ cm to a length of $39$ cm $.$

$($a$)$ How much work $($in J$)$ is needed to stretch the spring from $32$ cm to $34$ cm $?($Round your answer to two decimal places.$)$

$$ J

$($b$)$ How far beyond its natural length $($in cm $)$ will a force of $40$ N keep the spring stretched? $($Round your answer one decimal place.$)$

$36.$ cm

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$6.[0\mathrm{.}34/1$ Points$]$

$$ SCALC$95\mathrm{.}4\mathrm{.}011.$

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A spring has natural length $27$ cm $.$ Compare the work $($in J$)W_1$ done in stretching the spring from $27$ cm to $37$ cm with the work $($in J$)W_2$ done in stretching it from $37$ cm to $47$ cm $.($Use $k$ for the spring constant.$)$