The fastest time for the Sears Tower (now Willis Tower) stair climb (103 flights, or 2232 steps) is about 20 min.

a) Estimate the mechanical power in watts for a top climber. Assume the mass of climber is 80 kg and the heigth of the step is 0.18 m. Express your answer to two significant figures and include the appropriate units.

b) If the body is 20% efficient at converting chemical energy into mechanical energy, approximately how many joules and kilocalories of chemical energy does the body expend during the stair climb? Note: 1 food calorie = 1 kilocalorie = 4186 J.

a) 261.4 W b) 1, 568.5 kJ = 374.7 Kcal

Explanation:

In order to find out the mechanical power spent by a top climber, we need to find first the energy used to climb.

This energy is supplied by the body, and must be equal to the change in gravitational potential energy, as follows:

U = m. g. h

In order to find out the height (vertically) climbed, we need to multiply the height of one step times the quantity of steps.

The horizontal displacements along any step don't add to the total energy as the body does not work when moves horizontally.

So, h can be calculated as follows:

h = 0.18 m x 2,223 steps = 400.1 m

Replacing in (1), we have:

U = 80 kg. 9.8 m/s2.400. 1 m = 313.7 kJ

As we have the energy and the time used to spend the energy, we can get the power, as follows:

P = U / t = 313. 7 KJ / 1200 sec = 261.4 W

b) If only 20% of the chemical energy produced by the body is converted to the mechanical energy used to climb, this means that the chemical energy produced must be larger, as follows:

E = U / 0.2 = 313.7 kJ / 0.2 = 1,568.5 kJ

As 1 Kcal = 4,186 J, we have:

E (Kcal) = 1,568.5 kJ / 4,186 J = 374.7 Kcal