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Chapter 1: Problem 54

The rolling resistance of the tires, \(F_{r}\), opposing the motion of a vehicle is given by $$ F_{r}=f W $$ where \(f\) is a constant called the rolling resistance coefficient and \(W\) is the vehicle weight. For a vehicle weighing, \(W=300 \mathrm{kN}\) that is traveling at \(100 \mathrm{~km} / \mathrm{h}\), calculate the power in \(\mathrm{kW}\) required to overcome the vehicle rolling resistance for \(f=0.0070\).

Short Answer

Expert verified
The power required to overcome the rolling resistance of the vehicle is 58.338 kW.

Step by step solution

01

Calculate the Rolling Resistance

Given the weight, \( W \), of the vehicle is 300 kN (kilonewtons), and the rolling resistance coefficient, \( f \), is 0.0070. You have to calculate the rolling resistance, \( F_r \), using the formula provided, \( F_r = fW \) where \( F_r \) is the rolling resistance. Calculate \( F_r \) = 0.0070 * 300 kN = 2.1 kN
02

Convert Speed to m/s

The speed of the vehicle is given in km/h. This must be converted to m/s because in the standard unit for power (Watt or kilowatt), the speed must be in m/s. The conversion rate from km/h to m/s is achieved by dividing by 3.6. Hence, the speed is 100 km/hr = 100/3.6 = 27.78 m/s.
03

Calculate Power

The power, P, required to overcome the vehicle's rolling resistance is given by the formula \( P = Fv \), where \( P \) is the power, \( F \) is the force (the rolling resistance here) and \( v \) is the speed. Calculate \( P \) = 2.1 kN * 27.78 m/s = 58.338 kW

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