Question

The fuel burned by your car is directly proportional to the power required by your car’s engine or the power you use driving your car. For the operating conditions listed below, determine the minimum horsepower required by each. Use 900 kilograms as the mass of the car.

a. The car is traveling on a level road with a steady speed of 100 km/hr; the drag (air resistance) at this speed is 700 Newtons.

b. For the same conditions as question (a) the same car is traveling at the same speed and experiencing the same drag, but is now climbing a hill with a 5% grade.

c. The car is now back on the level road, but is accelerating from 100 km/hr to 120 km/hr. Because the speed increased the drag will also increase; therefore, calculate the increades drag as being proportional to the speed squared.

d. For the conditions of acceleration in (c), determine the power requirement for the car climbing the 5% grade hill.

Answer 1

(A) v =100 km/hr = 100 x 1000 m / 3600 s = 27.78 m/s

F = 700 N

P = F.v = 19444.44 W

(B) theta = tan^-1(0.05) = 2.86 deg

F = 700 + (900 x 9.81 x sin2.86) = 1140.9 N

P = 1140.9 x 27.78 = 31691.65 W

(C) 700 = b (27.7778^2)

b =0.907

Fdrag = 0.907 x (120 / 3.6)^2 = 1007.8 N

(D) F = 1007.8 + (900 x 9.81 x sin2.86) = 1448.3 N

P = 1448.3 x (120/3.6) = 48277 W