A $51-$kg woman eats a $571$ Calorie $(571$ kcal$)$ jelly doughnut for breakfast.

$($a$)$ How many joules of energy are the equivalent of one jelly doughnut?

J

$($b$)$ How many steps must the woman climb on a very tall stairway to change the gravitational potential energy of the woman$-$Earth system by a value equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is $15$ cm$.$

stairs

$($c$)$ If the human body is only $23\%$ efficient in converting chemical potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast?