Gasoline has an energy content of about 132.65 MJ/US Gallon. An average passenger car has a mass of 1500kg. The average vehicle experiences a drag force F(drag) = (0.176 kg/m)v^2, regardless of road conditions. A uniform and level road surface provides a 'rolling resistance' given by F(roll) = 0.018mg. Engine efficiency varies with the speed of the car, as shown in graph.
A) calculate the percent difference in the number of miles traveled by the car per gallon of gasoline consumed by the engine (mpg) when driving at 65 miles per hour(mph) vs. Driving at 75mph. Assume a uniform and level road surface. Calculate the percent difference in travel time when driving at 65mph instead of 75mph
B) calculate the percent difference in the mpg when driving at 65mph with tires that are 9 pounds per square inch (psi) below recommended pressure. Under pressure tires increases the rolling resistance of the car by 1% per 3psi below the recommended level. Assume a uniform and level road surface.
C) calculate the percent difference in the mpg when driving at 65mph a uniform and level road surface vs. Driving at 65mph on a road surface in poor condition. Poor surface conditions increase the rolling of the vehicle to F(roll) = 0.022mg.
Wncf = fd
KE = 1/2mv ^2
3. Attempt at solution
Part a) so the way I go about this I'm thinking I use the equation of sum of non conservative forces = kinetic energy. After doing some conversions, It would look something like work done by engine[132.65MJ * efficiency rate] - [drag force * d] - [roll force * d] = 1/2mv^2. Solve for d and use that to compare the distances. And would calculating the difference in travel time would it be just to compare the velocities once conversions are done?
Part b and c is similar to a but just make a couple of adjustments to some of the forces and stuff?
Am I on the right path on how to go about this or am I completely off?
I know this is kind of a long read but many thanks for any/all input. Definitely much appreciated
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