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Chapter 5: Problem 115

A \(100-\mathrm{kg}\) man decides to add to his exercise routine by walking up six flights of stairs \((30 \mathrm{~m}) 10\) times per day. He figures that the work required to increase his potential energy in this way will permit him to eat an extra order of French fries, at 245 Cal, without adding to his weight. Is he correct in this assumption?

Short Answer

Expert verified
By calculating the potential energy gained from walking up six flights of stairs 10 times a day, we find the total potential energy in calories. Comparing this value to the energy provided by an extra order of French fries (245 calories), we can determine whether the man's assumption is correct. \(PE = 100\,\text{kg} \times 9.81\,\text{m/s²} \times 30\,\text{m}\) and \(Total\: PE\: (\text{calories}) = \frac{Total\: PE\, (\text{Joules})}{4.184\, \text{J/cal}}\).

Step by step solution

01

Calculate the potential energy per flight of stairs

To start, we will find the potential energy (PE) gained by the man after walking up a single flight of stairs. Potential energy is given by the formula: \(PE = mgh\) where m is the mass of the man (100 kg), g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height of one flight of stairs (30 m). Therefore, we can calculate the potential energy as follows: \(PE = 100\,\text{kg} \times 9.81\,\text{m/s²} \times 30\,\text{m}\)
02

Calculate the total potential energy gained per day

Now that we have the potential energy gained per flight of stairs, we need to determine the total potential energy gained in a day. As the man walks up the stairs 10 times a day, we can multiply the potential energy gained per flight by 10: \(Total\: PE = 10 \times PE\)
03

Convert potential energy to calories

Now we need to convert the total potential energy from joules (the SI unit for energy) to calories because the energy content of French fries is given in calories. We know that: \(1\,\text{calorie} = 4.184\, \text{J}\) So we can convert the total potential energy to calories: \(Total\: PE\, (\text{calories}) = \frac{Total\: PE\, (\text{Joules})}{4.184\, \text{J/cal}}\)
04

Compare the energy from the potential energy gained to the energy provided by French fries

Now that we have the total potential energy in calories, we can compare it to the energy provided by an extra order of French fries (245 calories). If the total potential energy gained is greater than or equal to the energy from French fries, then the man's assumption is correct. You can evaluate whether the man's assumption is correct based on the comparison of energy gained and energy consumed.

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