$($a$)$ Calculate the force $($in N $)$ the woman in the figure below exerts to do a push$-$up at constant speed, taking all data to be known to three digits. $($You may need to use torque methods from a later chapter.$)$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$N$\}\backslash )$

$($b$)$ How much work $($in J$)$ does she do if her center of mass rises $0\mathrm{.}260$ m $?$

$81\mathrm{.}5$

$\backslash (\backslash$times $\backslash$quad $\backslash$mathrm$\{$J$\}\backslash )$

$($c$)$ What is her useful power output $($in W$)$ if she does $27$ push$-$ups in $1$ min? $($Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.$)$

w