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The summit of Mount Everest is \(8850 \mathrm{~m}\) above sea level. (a) How much energy would a \(90 \mathrm{~kg}\) climber expend against the gravitational force on him in climbing to the summit from sea level? (b) How many candy bars, at 1.25 MJ per 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

Expert verified
The climber expends about 7.81 MJ, requiring roughly 6 to 7 candy bars.

Step by step solution

01

Understanding the Problem

We need to calculate the gravitational potential energy required to move a climber of mass 90 kg from sea level to the summit of Mount Everest, which is 8850 meters high.
02

Formula for Gravitational Potential Energy

The formula to calculate gravitational potential energy is \(E = mgh\), where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity (approximately \(9.81\, m/s^2\) on Earth), and \(h\) is the height.
03

Calculation of Energy Expended

Substitute the given values into the formula: \[ E = 90 \, kg \times 9.81 \, m/s^2 \times 8850 \, m. \] This computes to \[ E = 7,810,050 \, J. \] Thus, the energy expended is approximately \(7.81 \, MJ\).
04

Calculate the Number of Candy Bars Required

Each candy bar provides 1.25 MJ of energy. To find out how many candy bars are needed, divide the total energy by the energy per candy bar: \[ \text{Number of candy bars} = \frac{7.81 \, MJ}{1.25 \, MJ/bar} \approx 6.25. \] Hence, approximately 6 to 7 candy bars are needed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mount Everest
Mount Everest, the highest peak on Earth, towers at 8,850 meters above sea level. Climbing to such a great height is no small feat and requires a significant energy investment. However, the spectacular challenge of ascending Mount Everest is not merely about the height. It also involves dealing with harsh weather conditions, low oxygen levels, and treacherous terrain.
Understanding the energy aspects of such a climb helps us appreciate the massive physical challenge climbers face. The gravitational potential energy, which depends on both the mass of the climber and their ascent height, embodies a crucial part of the total effort. However, it's only a fraction of the energy that climbers actually expend during their ascent, encompassing not just altitude but also endurance, nutrition, and survival skills.
energy expenditure
Energy expenditure in climbing is more complex than it initially appears. At a glance, one might think that lifting a body against gravity accounts for most of the energy used. However, a climber requires additional sources of energy for various bodily functions and meeting environmental challenges throughout the climb.
  • The movement at high altitudes is less efficient than at sea level, demanding extra energy for the same physical actions.
  • The body requires more energy at higher altitudes to maintain optimum warmth.
  • Combatting fatigue and supporting continuous muscle function over long periods also use substantial energy reserves.
Hence, the visible physical output does not tell the complete story of energy expenditure, as the body is continuously adjusting and compensating for the diverse harsh conditions presented by Mount Everest.
work against gravity
Work against gravity is about moving a mass upwards within a gravitational field. For Mount Everest's climbers, this work can be quantified using the gravitational potential energy formula: \[E = mgh\] where \(m\) is mass, \(g\) is the gravity acceleration (around 9.81 m/s² on Earth), and \(h\) is the height.
Climbing to the summit involves doing work against Earth's gravity by increasing their gravitational potential energy. Here, for a 90 kg climber rising to 8,850 meters, energy needed is calculated to be approximately 7.81 MegaJoules (MJ).
However, this is just the theoretical energy needed to lift the climber straight up against gravity. Actual conditions entail a lot more energy expenditure due to extra physical exertion, path circumference, rest periods, and climactic factors. The calculated gravitational energy is a small fragment of the total energy spent during a climb, highlighting that other physiological and environmental factors play significant roles as well.

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Most popular questions from this chapter

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