Question

A kinesiology student competed in the Du Bois Library Tower Run last Fall while measuring his oxygen consumption by wearing a portable respirometer. The student had a mass of 73 kg and the Du Bois library has 440 steps with a vertical rise of 17.9 cm per step. It took him 140 s to complete the tower run. Based on this information, determine how much mechanical work the student did. From his oxygen consumption it was estimated that he expended metabolic energy at a rate of 22.3 kcal/min while running up the stairs. Based on this information, determine his percent movement efficiency (Hint: 1 J = 0.000239 Kcals).

Mechanical work:
Efficiency (%):

Answer 1

The student did 56239.92 J of mechanical work while climbing the stairs. The percent movement efficiency of the student is 74.73%.

Step-by-step explanation:

To determine the mechanical work done by the student, we need to calculate the gravitational potential energy gained by climbing the stairs. The vertical rise of each step is given as 17.9 cm. Therefore, the total vertical distance climbed is 440 steps * 17.9 cm = 7886 cm = 78.86 m.

The work done to climb the stairs is given by the formula: W = mgh, where m is the mass of the student, g is the acceleration due to gravity, and h is the height. Plugging in the values, we get: W = (73 kg)(9.8 m/s^2)(78.86 m) = 56239.92 J.

To determine the efficiency, we need to calculate the metabolic energy expended by the student. The rate of energy expenditure is given as 22.3 kcal/min. To convert this to joules, we use the conversion factor: 1 J = 0.000239 kcal. Therefore, the rate of energy expenditure in joules is: (22.3 kcal/min)(0.000239 kcal/J) = 0.00534 J/s.

The efficiency is given by the formula: Efficiency = Useful work output / Energy input. Plugging in the values, we get: Efficiency = (56239.92 J) / (0.00534 J/s * 140 s) = 74.73%.