Question

A 53 kg person eats a 518 Calorie (518 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of this jelly doughnut? (b) How many steps must this person climb on a very tall stairway to change the gravita- tional potential energy of the person-Earth system by a value equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is h = 15 cm. (c) If the human body is only 22% efficient in converting chemical potential energy to mechanical energy, how many steps must the person climb to work off this delicious, amazing breakfast, and how tall of a staircase does this correspond to?

Answer 1

Answer:

A. 2,168,399.8 J

B. 27832 steps

C. 918.5 m with 6123 steps

Explanation:

A. Since 1 cal equals to 4.1868 joules

$E=518\,kcal*\frac{1000\,cal}{1\,kcal} *\frac{4.1868\,J}{cal} =2,168,399.8\,J$

B. The change in the gravitational potential energy of the system is given by

$U_{G} =mgz$

Being m the mass of the person, g the gravity constant and z the height difference. The required z is then given by:

$z=\frac{U_{G} }{mg} = \frac{2,168,399.8\,J}{53\,kg*9.8\,m/s^{2} } =4174.8 \,m$

Changed to 0.15 m stairs:

$steps=\frac{4174.8\,m}{0.15\,m} =27832\,steps$

C. At 22% efficiency, the values are reduced, since the process is less efficient:

$steps=27832\,steps*0.22=6123$

$z=4174.8\,m*0.22=918.5\,m$