You have been asked to test drive a car and study its actualperformance relative

Question

You have been asked to test drive a car and study its actualperformance relative to its specifications. This particular car'sengine is rated at 173 hp. This valueis the peak rating, which means that it is capable, atmost, of providing energy at the rate of 173 hp to the drive wheels. You determine that thecar's mass (including test equipment and driver on board) is938 kg. (a) When cruising at a constant 55 mi/h youronboard engine-monitoring computer determines that the engine isproducing 13.6 hp. From previouscoasting experiments, it has been determined that the coefficientof rolling friction on the car is 0.0195. Assume that the drag force on the carvaries as the square of the car's speed. That is,Fd = Cv2. What isthe value of the constant, C?
1 kg/m

(b) Considering the peak power, what is the maximum speed (to thenearest 1 mi/h) that you would expect the car could attain? (Thisproblem can be done by hand analytically, but it can be done moreeasily and quickly using a graphing calculator or spreadsheet.)
2 mi/h (a) When cruising at a constant 55 mi/h youronboard engine-monitoring computer determines that the engine isproducing 13.6 hp. From previouscoasting experiments, it has been determined that the coefficientof rolling friction on the car is 0.0195. Assume that the drag force on the carvaries as the square of the car's speed. That is,Fd = Cv2. What isthe value of the constant, C?
1 kg/m

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

Explanation / Answer

1. The net opposing force is friction + drag = mg + Cv^2 Power required = force * speed = (mg + Cv^2)v = 13.6 hp =13.6*745.7 watts for v = 55 mph = 55*.447 m/s = 24.585 m/s C = ((13.6*745.7)/v -mg)/v^2 = ((13.6*745.7)/24.585-.0195*938*9.8)/24.585^2 = .386 Ns^2/m^2 2. for peak power 173 hp, v would be given by (mg + Cv^2)v = 173 hp = 173*745.7 watts solving this by a graphing calculator, v = 67.167 m/s = 150.3 mph

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