The record time for a Tour de France cyclist to ascend the famed 1100-m-high Alpe d'Huez was 37.5 min, set by Marco Pantani in 1997. Pantani and his bike had a mass of 65 kg. Assume the body works with 25 % efficiency.
A)How many Calories did he expend during this climb?
B)What was his average metabolic power during the climb?
no
Cuck
To answer these questions, we need to calculate the amount of work done during the climb and then use that to determine the energy expenditure (in calories) and average metabolic power.
A) To calculate the work done, we can use the formula:
work = force * distance * cos(theta)
where force = mass * gravity * sin(theta), distance = height of the climb, and theta = angle of the incline.
Given:
mass (m) = 65 kg
height (distance) = 1100 m
angle of incline (theta) = 0 degrees (as we assume a horizontal road)
gravity (g) = 9.8 m/s^2
First, let's calculate the force:
force = mass * gravity * sin(theta)
= 65 kg * 9.8 m/s^2 * sin(0)
= 0 N (since sin(0) = 0)
Now, let's calculate the work:
work = 0 N * 1100 m * cos(0)
= 0 J (since cos(0) = 1)
Since there is no work done against gravity in a horizontal road, the work done is zero. Therefore, the energy expenditure will also be zero.
B) To calculate the average metabolic power, we need to convert the work done into watts (W). We can use the formula:
power = work / time
Given that the time taken to climb the Alpe d'Huez was 37.5 minutes (or 2250 seconds), we substitute the values:
power = 0 J / 2250 s
= 0 W (since any value divided by zero is undefined)
Again, since the work done is zero, the average metabolic power will be zero.
So, in conclusion, the cyclist did not expend any calories during the climb and his average metabolic power was zero. This may seem counterintuitive, but it is because the climb was on a horizontal road and therefore no work was done against gravity.
gain in potential = m g h
= 65 * 9.81 * 1100 Joules
eff = ..25
so
.25 energy = 65* 9.81 * 1100
so energy expended = 4*65*9.81*1100
Joules
4184 Joules = 1000 calories
so in Calories
(4/4.184)65*9.81*1100
power = energy expended/ time
in watts = 4*65*9.81*1100/(37.5*60)