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Chapter 10: Problem 46

The physical fitness of athletes is measured by \(^{u} V_{\mathrm{O}_{2}} \max _{2}^{\prime \prime}\) which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a \(V_{\mathrm{O}_{2}}\) max of 45 \(\mathrm{mL} \mathrm{O}_{2 / \mathrm{kg}}\) body mass/min, but a world-class male athlete can have a \(V_{\mathrm{O}_{2}}\) max reading of 88.0 \(\mathrm{mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in 1 by an average man who weighs 185 lbs and has a \(V_{\mathrm{O}_{2}}\) max reading of 47.5 \(\mathrm{mLO}_{2} / \mathrm{kg}\) body mass/min. (b) If this man lost \(20 \mathrm{lb},\) exercised, and increased his \(V_{\mathrm{O}_{2}}\) max to 65.0 \(\mathrm{mL}\) O \(_{2} / \mathrm{kg}\) body mass/min, how many mL of oxygen would he consume in 1 \(\mathrm{hr}\) ?

Short Answer

Expert verified
Initially, the man weighs 185 lbs, which converts to \(Weight_{kg} = \frac{185}{2.205} \approx 83.9kg\). The volume of oxygen consumed in 1 min is \(Volume_{1min} = 47.5 \cdot 83.9 \approx 3985.25 mL\). After losing 20 lbs, the new weight is \(New Weight_{kg} = \frac{185 - 20}{2.205} \approx 74.8 kg\). With a \(V_{O_2}\) max of 65.0 \(\mathrm{mLo}_{2} / \mathrm{kg}\), the volume of oxygen consumed in 1 min is \(Volume_{new1min} = 65.0 \cdot 74.8 \approx 4862.0 mL\), and in 1 hour, the volume is \(Volume_{1hr} = 4862.0 \cdot 60 \approx 291720 mL\).

Step by step solution

01

Convert weight to kg

We need to convert the man's weight from lbs to kg, as the \(V_{O_2}\) max is given in \(mL \cdot O_2 / kg \cdot min\). We are given: - Initial weight: 185 lbs - Weight loss: 20 lbs First, let's find the initial weight in kg: \(Weight_{kg} = \frac{Weight_{lbs}}{2.205}\)
02

Calculate the volume of oxygen consumed in 1 min initially

We are given that the \(V_{O_2}\) max of the man initially is 47.5 \(\mathrm{mLO}_{2} / \mathrm{kg}\) body mass/min. Now we can use the initial weight in kg, obtained in Step 1, and the \(V_{O_2}\) max formula to find the volume of oxygen consumed in 1 minute: \(Volume_{1min} = V_{O_2} \cdot Weight_{kg}\)
03

Calculate the weight after the weight loss

Now we can find the man's weight after losing 20 lbs. This new weight will be used to calculate the volume of oxygen consumed after increasing the \(V_{O_2}\) max: \(New Weight_{kg} = \frac{Initial Weight_{lbs} - Weight Loss_{lbs}}{2.205}\)
04

Calculate the volume of oxygen consumed in 1 hr with the increased \(V_{O_2}\) max

We are given that the new \(V_{O_2}\) max of the man after weight loss and exercising is 65.0 \(\mathrm{mLo}_{2} / \mathrm{kg}\) body mass/min. Now we can use the new weight in kg, obtained in Step 3, and the new \(V_{O_2}\) max formula to find the volume of oxygen consumed in 1 minute: \(Volume_{new1min} = New V_{O_2} \cdot New Weight_{kg}\) Now, to find the volume of oxygen consumed in 1 hour, we need to multiply the volume consumed in 1 minute by the number of minutes in an hour: \(Volume_{1hr} = Volume_{new1min} \cdot 60\)

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