Question

Be sure to answer all parts. A 45−kg person drinks 5.0 × 102 g of milk, which has a caloric value of approximately 3.0 kJ/g. If only 17 percent of the energy in milk is converted to mechanical work, how high (in meters) can the person climb based on this energy intake? Enter your answer in scientific notation. Hint: The work done in ascending is given by mgh, where m is the mass (in kg), g is the gravitational acceleration (9.8 m/s2), and h is the height (in meters).

__ × 10 __ m

Answer 1

Mechanical energy obtained from the milk = mass of milk * calorific value * % converted to mechanical work

= 500 * 3.0 * 17 / 100 = 255 KJ = 2.55 * 10⁵ J

Mechanical energy of milk = potential energy due to gravity = mass of person * g * height (h)

2.55 * 10⁵ = 45 * 9.8 * h

SOlving, h = 578.23 meters = 5.78 * 10² m