Problem $2.$ Charging a cellphone.

The power is out and you need to charge up your cell phone. Fortunately, you have a hand cranked generator that is very efficient at converting mechanical energy into electrical energy of the battery, $\backslash (\backslash$eta $\backslash$rightarrow $1\backslash ).$ The generator is effectively a handle that you rotate around in a circle by applying a force.

$($a$)$ If the handle has a radius of rotation of $10$ cm and you can crank it at a rate of $1$ revolution per second by applying a $50$ N force tangentially$,$ how much power are you generating?

$($b$)$ With the power you calculated in $($a$),$ how long will it take you to charge up your phone? A typical phone battery has a capacity of about $10$ Watt$-$hours.

$($c$)$ How many food calories would you need to consume to produce this much output energy? Include an approximate metabolic efficiency for humans.

$($d$)$ If you had a $\backslash (0\mathrm{.}1\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ solar panel, how long would it take to charge the phone? Include a typical solar panel efficiency and assume you're charging on a bright sunny day.