A $290$ g block is dropped onto a relaxed vertical spring that has a spring constant of $\backslash ($ k$=2\mathrm{.}2\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$cm$\}\backslash )($see the figure$).$ The block becomes attached to the spring and compresses the spring $11$ cm before momentarily stopping. While the spring is being compressed, what work is done on the block by $($a$)$ the gravitational force on it and $($b$)$ the spring force? $($c$)$ What is the speed of the block just before it hits the spring? $($Assume that friction is negligible.$)($d$)$ If the speed at impact is doubled, what is the maximum compression of the spring?

$($a$)$ Number

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$($b$)$ Number

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$($c$)$ Number

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$($d$)$ Number

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