The physical fitness of athletes is measured by \({ }^{4} V_{\mathrm{O}_{2}}\) max," 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 \(/ \mathrm{min}\), 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 \(1 \mathrm{hr}\) by an average man who weighs \(85 \mathrm{~kg}\) and has a \(V_{\mathrm{O}_{2}}\) max reading of \(47.5 \mathrm{~mL}\) $\mathrm{O}_{2} / \mathrm{kg}\( body mass \)/ \mathrm{min} .(\mathbf{b})\( If this man lost \)10 \mathrm{~kg},\( exercised, and increased his \)V_{\mathrm{O}_{2}}\( max to \)65.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\( body mass \)/ \mathrm{min}$, how many mL of oxygen would he consume in \(1 \mathrm{hr} ?\)

Step by step solution

01

1. Calculate the oxygen consumption rate:

Multiply the man's weight (85 kg) with his \(V_{\mathrm{O}_{2}}\) max reading (47.5 mL O₂/kg/min): Oxygen consumption rate = \(85 \mathrm{~kg} * 47.5 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg} / \mathrm{min} = 4037.5 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{min}\).

02

2. Convert the rate from minutes to hours:

Multiply the oxygen consumption rate (4037.5 mL O₂/min) by the number of minutes in an hour (60 min): Total oxygen consumption in 1 hr = \(4037.5 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{min} * 60 \mathrm{~min} / \mathrm{hr} = 242250 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{hr}\). # b) Calculate the oxygen consumed in 1 hr after weight loss and \(V_{\mathrm{O}_{2}}\) max increase#:

03

1. Update the weight and \(V_{\mathrm{O}_{2}}\) max readings:

Subtract 10 kg from the initial weight (85 kg): New weight = \(85 \mathrm{~kg} - 10 \mathrm{~kg} = 75 \mathrm{~kg}\). Update the \(V_{\mathrm{O}_{2}}\) max reading to 65.0 mL O₂/kg/min.

04

2. Calculate the new oxygen consumption rate:

Multiply the new weight (75 kg) with the new \(V_{\mathrm{O}_{2}}\) max reading (65.0 mL O₂/kg/min): New oxygen consumption rate = \(75 \mathrm{~kg} * 65.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg} / \mathrm{min} = 4875 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{min}\).

05

3. Convert the new rate from minutes to hours:

Multiply the new oxygen consumption rate (4875 mL O₂/min) by the number of minutes in an hour (60 min): New total oxygen consumption in 1 hr = \(4875 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{min} * 60 \mathrm{~min} / \mathrm{hr} = 292500 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{hr}\). So, in the first case, the man consumes 242250 mL O₂/hr, and in the second case, he consumes 292500 mL O₂/hr.

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