Related questions with answers

The two major forces opposing the motion of a vehicle moving on a level road are the rolling resistance of the tires, FrF_{r}, and the aerodynamic drag force of the air flowing around the vehicle, FdF_{d}, given respectively by

Fr=fw,Fd=CdA212ρV2F_{r}=f w, \quad F_{d}=C_{d} A_{2} \frac{1}{2} \rho V^{2}

where ff and CdC_{d} are constants known as the rolling resistance coefficient and drag coefficient, respectively, ww and A are the vehicle weight and projected frontal area, respectively, V is the vehicle velocity, and ρ\rho is the air density. For a passenger car with w=3040w=3040 \:lbf, A=6.24ft2A=6.24 \: ft^2 , and Cd=0.25C_{d}=0.25, and when f=0.02f= 0.02 and ρ=0.08lb/ft3\rho=0.08 \: lb/ft^3

(a) determine the power required, in hp, to overcome rolling resistance and aerodynamic drag when V is 55 mi/h.(b) plot versus vehicle velocity ranging from 0 to 75 mi/h (i) the power to overcome rolling resistance, (ii) the power to overcome aerodynamic drag, and (iii) the total power, all in hp.\begin{array}{l l } \text{(a) determine the power required, in hp, to overcome rolling resistance and aerodynamic drag when V is 55 mi/h.}\\ \text{(b) plot versus vehicle velocity ranging from 0 to 75 mi/h (i) the power to overcome rolling resistance, (ii) the power to overcome aerodynamic drag, and (iii) the total power, all in hp.}\\ \end{array}

What implication for vehicle fuel economy can be deduced from the results of part (b)?

Question

A major force opposing the motion of a vehicle is the rolling resistance of the tires, FrF_{r}, given by

Fr=fwF_{\mathrm{r}}=f w

where ff is a constant called the rolling resistance coefficient and ww is the vehicle weight. Determine the power, in kW, required to overcome rolling resistance for a truck weighing 322.5 kN that is moving at 110 km/h. Let f=0.0069f =0.0069.

Solution

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Given:

Fr=fW˙F_r=f \cdot \dot W W=322.5 kN=322.5×103 NW=322.5 \space \text{kN}=322.5 \times 10^3 \space \text{N} V=110 kmh=30.55 msV=110 \space \frac{\text{km}}{\text{h}}=30.55 \space \frac{\text{m}}{\text{s}} f=0.0069f=0.0069

The rolling resistance of the tires of a vehicle is given by Fr=fWF_r=f \cdot W. The power required to overcome rolling resistance is to be determined.

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