You have been asked to test drive a car and study its actual performance relativ

Question

You have been asked to test drive a car and study its actual performance relative to its specifications. This particular car's engine is rated at 180 hp. This value is thepeak rating, which means that it is capable, at most, of providing energy at the rate of 180 hp to the drive wheels. You determine that the car's mass (including test equipment and driver on board) is 1336 kg.

(a) When cruising at a constant 55 mi/h your onboard engine-monitoring computer determines that the engine is producing 14.5 hp. From previous coasting experiments, it has been determined that the coefficient of rolling friction on the car is 0.0137. Assume that the drag force on the car varies as the square of the car's speed. That is, Fd = Cv2. What is the value of the constant, C?

________kg/m

(b) Considering the peak power, what is the maximum speed (to the nearest 1 mi/h) that you would expect the car could attain? (This problem can be done by hand analytically, but it can be done more easily and quickly using a graphing calculator or spreadsheet.)
________mi/h

Explanation / Answer

1. The net opposing force is Ffriction + drag = mg + Cv^2

Power required = force * speed

P = (mg + Cv^2)v

P = 14.5 hp

P =14.5*745.7

P = 10812. 65 watts

1 mph =   0.4470 m/s

for v = 55 mph = 55*0.447 m/s

v = 24.585 m/s

C = ((10812.65)/v -mg)/v^2

C = ((10812.65)/24.585-0.0137*1336*9.8)/24.585^2

C = 0.43 Kg/m (answer)
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2. for peak power 180 hp,

v would be given by

(mg + Cv^2)v = 180 hp

P = 180*745.7

P = 134226 watts

solving this by a graphing calculator,

(mg + Cv^2)v = 134226

(0.0137 * 1336 * 9.81) + (0.43 * 24.858^2)* v = 134226

v = 301.45 m/s or 674.38   mi/hr (answer)

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