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Evaluating WorkThe two major forces opposing the motion of
Chapter 2, Problem 22P(choose chapter or problem)
The two major forces opposing the motion of a vehicle moving on a level road are the rolling resistance of the tires, \(F_{\mathrm{r}}\), and the aerodynamic drag force of the air flowing around the vehicle, \(F_{\mathrm{d}}\), given respectively by
\(F_{\mathrm{r}}=f q, \quad F_{\mathrm{d}}=C_{\mathrm{d}} \mathrm{A} \frac{1}{2} \rho \mathrm{V}^2\)
where f and \(C_{\mathrm{d}}\) are constants known as the rolling resistance coefficient and drag coefficient, respectively, W and A are the vehicle weight and projected frontal area, respectively, V is the vehicle velocity, and \(\rho\) is the air density. For a passenger car with \(\mathscr{W}=3550 \mathrm{lbf}, \mathrm{A}=23.3 \mathrm{ft}^2\), and \(C_{\mathrm{d}}=0.34\), and when f=0.02 and v\rho=0.08 \mathrm{lb} / \mathrm{ft}^3\)
(a) determine the power required, in hp, to overcome rolling resistance and aerodynamic drag when V is \(55 \mathrm{mi} / \mathrm{h}\).
(b) plot versus vehicle velocity ranging from 0 to \(75 \mathrm{mi} / \mathrm{h}\) (i) the power to overcome rolling resistance, (ii) the power to overcome aerodynamic drag, and (iii) the total power, all in hp.
What implication for vehicle fuel economy can be deduced from the results of part (b)?
Questions & Answers
QUESTION:
The two major forces opposing the motion of a vehicle moving on a level road are the rolling resistance of the tires, \(F_{\mathrm{r}}\), and the aerodynamic drag force of the air flowing around the vehicle, \(F_{\mathrm{d}}\), given respectively by
\(F_{\mathrm{r}}=f q, \quad F_{\mathrm{d}}=C_{\mathrm{d}} \mathrm{A} \frac{1}{2} \rho \mathrm{V}^2\)
where f and \(C_{\mathrm{d}}\) are constants known as the rolling resistance coefficient and drag coefficient, respectively, W and A are the vehicle weight and projected frontal area, respectively, V is the vehicle velocity, and \(\rho\) is the air density. For a passenger car with \(\mathscr{W}=3550 \mathrm{lbf}, \mathrm{A}=23.3 \mathrm{ft}^2\), and \(C_{\mathrm{d}}=0.34\), and when f=0.02 and v\rho=0.08 \mathrm{lb} / \mathrm{ft}^3\)
(a) determine the power required, in hp, to overcome rolling resistance and aerodynamic drag when V is \(55 \mathrm{mi} / \mathrm{h}\).
(b) plot versus vehicle velocity ranging from 0 to \(75 \mathrm{mi} / \mathrm{h}\) (i) the power to overcome rolling resistance, (ii) the power to overcome aerodynamic drag, and (iii) the total power, all in hp.
What implication for vehicle fuel economy can be deduced from the results of part (b)?
ANSWER:a)
Step 1 of 5
We have to determine the power required, in hp to overcome rolling resistance and aerodynamic drag for a vehicle when is 55 mi/h.
The power required to overcome the rolling resistance can be calculated using the expression
where,
The rolling resistive force in N
velocity of the vehicle = 55 mi/h
The rolling resistive force is given by
where. rolling resistance coefficient = 0.02
weight of the vehicle = 3550 lbf
Thus,
