Fundamentals of Transportation/Grade/Homework

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1. Determine the maximum grade an empty tractor-trailer with a mass of 10000 kg can climb at a sustained speed of 75 km/h.

The frontal area (A) of the truck is 10 m2, the drag coefficient = 1.00 and the available power is 280 kW, ρ=1.2 kg*m−3, g = 9.81 m*sec−2

2. What is the maximum grade a bicycle can climb at a sustained speed of 12 km/h assuming the following:

  • Rho = density of air (1.20 kg*m−3)
  • g = 9.81 m*sec−2
  • Mass (with bicyclist) = 100 kg
  • Nominal Power = 1 kW
  • Frontal Area (A) = 1 m2
  • Drag Coefficient = 0.5
  • Available power = 100 percent of nominal power
  • Fr = 0.020 W

3. Bicyclists get tired. Assume the bicyclist slowly loses power (and thus velocity) going up the hill of the grade you just determined in question 2 above. If available power drops continuously from 100% to 0% over the course of the hour, to the nearest kilometer, how far does the bicyclist travel? (Use appropriate approximations.)