Question

The summit of Mount Everest is 8850 mabove sea level. (a) How much energy would a 90 kgclimber expand against the gravitational force on him in climbing to the summit from sea level? (b) How many candy bars, at 1.25 MJper bar, would supply an energy equivalent to this? Your answer should suggest that work done against the gravitational force is a very small part of the energy expended in climbing a mountain.

Short answer

1. The energy that the climber expands to work against the gravitational force is$7.8\times {10}^6\mathrm{J}$
2. Number of candy bars required are 6 bar .

Step-by-step solution

The given data

The mass of the climber is, m = 90 kg

The energy that the climber gets per bar, E = 1.25 MJ $\left(\frac{{10}^6\mathrm{MJ}}{1\mathrm{MJ}}\right)=1.25\times {10}^6\mathrm{J}$

The height of the summit of Mount Everest, h = 8850 m

The acceleration due to gravity is,$\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$

Understanding the concept of energy

The energy of the climber against the gravitational force from the sea level shows the results that there is a change in potential energy.

Formula:

Change in potential energy, $∆\mathrm{PE}=\mathrm{mg}\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)$ (1)

a) Calculation of the energy expended by the climber to climb the height

The work or energy expanded by the climber to go against the gravitational force to climb to the summit of the mountain is given using equation (1):

W = Change in potential energy

$$\begin{gathered} =90\mathrm{kg}\times 9.8\mathrm{m}/{\mathrm{s}}^2\times \left(8850\mathrm{m}-0\mathrm{m}\right) \\ =7.8\times {10}^6\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2\left(\frac{1\mathrm{J}}{1\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2}\right) \\ =7.8\times {10}^6\mathrm{J} \end{gathered}$$

Hence, the value of the energy is$7.8\times {10}^6\mathrm{J}$ .

b) Calculation of the required candy bars to consume that energy in part (a)

The number of candy bars that are required by the climber to supply energy is given as:

$$\begin{gathered} \mathrm{n}=\frac{7.8\times {10}^6\mathrm{J}}{1.25\times {10}^6\mathrm{J}/\mathrm{bar}} \\ =6.2\mathrm{bar} \\ \approx 6\mathrm{bar} \end{gathered}$$

Hence, the required candies are 6 bar .