Who is working harder, Fred running a 10 min mile pace at a 10% grade or Pete who is 55 kg, cycling on a Monarch ergometer with a resistance of 2.5 kg and a pedal rate of 60 rpm?
To determine who is working harder between Fred running on a 10% grade at a 10 min mile pace and Pete cycling on a Monarch ergometer, we need to consider their respective intensities and energy expenditures.
First, let's calculate Fred's intensity. Running on a 10% grade means that Fred is running uphill, which requires more effort compared to running on a flat surface. The steeper the grade, the harder the workout. Running a 10-minute mile pace means Fred is covering one mile in 10 minutes, which translates to 6 miles per hour (mph). To determine the intensity, we need to account for the pace and the grade.
To calculate running intensity, we can use the "grade-adjusted pace" (GAP) formula:
GAP (in mph) = Flat Pace (in mph) + (Grade * 0.01 * Flat Pace)
Given that Fred's flat pace is 6 mph and the grade is 10%, we can substitute these values into the equation:
GAP = 6 mph + (10% * 0.01 * 6 mph)
GAP = 6 mph + (0.1 * 0.06 mph)
GAP = 6 mph + 0.006 mph
GAP ≈ 6.006 mph
Therefore, Fred's intensity while running at a 10 min mile pace on a 10% grade is approximately 6.006 mph.
Now let's calculate Pete's intensity while cycling on the Monarch ergometer. The intensity of cycling can be determined by the resistance and pedal rate.
To calculate intensity, we can use the following formula:
Intensity (in watts) = (Pedal Rate * Resistance * 6.12) + 6.4
Given that Pete's pedal rate is 60 rpm and the resistance is 2.5 kg, we can substitute these values into the equation:
Intensity = (60 rpm * 2.5 kg * 6.12) + 6.4
Intensity = (183) + 6.4
Intensity ≈ 189.4 watts
Therefore, Pete's intensity while cycling on the Monarch ergometer is approximately 189.4 watts.
To determine who is working harder between Fred and Pete, we need to compare their intensities. In this case, Pete's cycling intensity of 189.4 watts is higher than Fred's running intensity of 6.006 mph.
Therefore, based on the given information, Pete is working harder than Fred.
To determine who is working harder, we need to calculate the energy expenditure for both Fred and Pete.
Energy expenditure for Fred:
1. Calculate the distance Fred runs in 1 hour:
- 10 min/mile = 6 miles/hour
2. Calculate the work done by Fred against the 10% grade:
- Work = Force x Distance
- Force = Weight x Grade
- Weight = 55 kg
- Grade = 10% = 0.1
- Distance = 6 miles = 6 x 1609.34 meters (assuming each mile is 1609.34m)
- Work = 55 kg x 9.8 m/s^2 x 0.1 x 6 x 1609.34 m
3. Calculate the energy expenditure:
- Energy Expenditure (in joules) = Work
Energy expenditure for Pete:
1. Calculate the work done by Pete against the resistance:
- Work = Force x Distance
- Force = Weight of the ergometer + Force applied by Pete on the ergometer
- Weight of the ergometer = 2.5 kg
- Distance = 60 revolutions/minute x 60 minutes (assuming 1 revolution covers a distance equal to the circumference of the pedal’s circle)
- Work = (55 kg + 2.5 kg) x 9.8 m/s^2 x Distance
2. Calculate the energy expenditure:
- Energy Expenditure (in joules) = Work
After calculating the energy expenditure for both Fred and Pete, we can determine who is working harder by comparing the values.