Megan is out training on her bike and decides to ride up Big Cottonwood Canyon.
ID: 1517113 • Letter: M
Question
Megan is out training on her bike and decides to ride up Big Cottonwood Canyon. The mass of Megan and her bike is 80 kg. She has a CdA (drag area) of 0.3 m2 and the coefficient of rolling resistance (Crr) between her bike and the road is 0.003. During her ride the average air density was 0.98 kg/m3 and winds were calm. The road is 29 km long and ascends 900 m. Megan completes this ride in 2 hours at an RER of 1.0. We also know her efficiency is 24%.
a.How much total mechanical work did Megan do (in kJ)?
b. What was her average power over the duration of the ride?
Explanation / Answer
Here ,
mass of bike ,m = 80 Kg
CdA = 0.3 m^2
k = 0.003
air density , p = 0.98 Kg/m^3
speed of bike . v = 29000/(2 * 3600)
v = 4.03 m/s
Fd = 0.5 * p * v^2 * Cd * A
Fd = 0.5 * 0.98 * 4.03^2 * 0.3 * 0.003
Fd = 7.16 *10^-3 N
Now, for the total mechnical work = m * g * h + Fd * distance
total mechnical work = 80 * 9.8 * 900 + 7.16 *10^-3 * 29000
total mechnical work = 705807.6 J
the total mechnical work is 705807.6 J
b) power of Megan = total mechcanical work/(time * efficiency)
power of Megan = 705807.6/(2 * 3600 * 0.24)
power of Megan = 408.5 W
the power of Megan is 408.5 W