A \(201-\) lb man decides to add to his exercise routine by walking up three flights of stairs \((45 \mathrm{ft}) 20\) 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
The man's assumption is incorrect. Climbing the stairs 20 times a day only burns 244,235.2 Joules, while the energy gained from eating an extra order of French fries is 1,025,020 Joules. Thus, the work done is not sufficient to burn off the additional calories gained from the French fries.

Step by step solution

01

Calculate the work done in climbing stairs

To calculate the work done by the man in climbing one flight of stairs, we will use the formula for gravitational potential energy, which is: \(PE = m \cdot g \cdot h\) where PE is the potential energy, m is the mass in kilograms, g is the acceleration due to gravity (\(9.81 m/s^2\)), and h is the height in meters. First, we need to convert the man's weight from pounds to kilograms and the height from feet to meters: - Weight in kg: \(201 \, lb \cdot \frac{1 \, kg}{2.205 \, lb} \approx 91.16 \, kg\) - Height in m: \(45 \, ft \cdot \frac{1 \, m}{3.281 \, ft} \approx 13.72 \, m\) Now we can calculate the gravitational potential energy: \(PE = 91.16 \, kg \cdot 9.81 \frac{m}{s^2} \cdot 13.72 \, m \approx 12211.76 \, J\) The work done in climbing three flights of stairs once is 12211.76 Joules.
02

Calculate the work done in climbing stairs 20 times

Now we will multiply this by 20 to find the total work done in climbing the stairs 20 times a day: Total work done: \(12211.76 \, J \cdot 20 = 244235.2 \, J\)
03

Convert French fries calories to Joules

We'll convert the energy gained from the extra order of French fries from calories to Joules: 1 Calorie = 1 kcal (1 kilocalorie) = 4184 Joules Energy gained: \(245 \, Cal \cdot 4184 \frac{J}{Cal} \approx 1025020 \, J\)
04

Compare the work done with the energy gained

Finally, we will compare the total work done by the man with the energy gained from the fries: Work done: 244235.2 J Energy gained: 1025020 J As we can see, the energy gained from eating the extra serving of French fries (1025020 J) is much greater than the work done in climbing the stairs 20 times (244235.2 J). Therefore, the man's assumption is not correct, and climbing the stairs 20 times per day will not allow him to eat the extra serving of French fries without adding to his weight.

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