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

$$F_{r}=f w, \quad F_{d}=C_{d} A_{2} \frac{1}{2} \rho V^{2}$$

where $f$ and $C_{d}$ 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 $w=3040 \:$lbf, $A=6.24 \: ft^2$ , and $C_{d}=0.25$, and when $f= 0.02$ and $\rho=0.08 \: lb/ft^3$

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

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

A force P of 70 N is applied by a rider to the front hand brake of a bicycle (P is the resultant of an evenly distributed pressure). As the hand brake pivots at A, a tension T develops in the 460-mm long brake cable $\left(A_{e}=\right.$ $1.075\ \mathrm{mm}^{2} )$ which elongates by $\delta=0.214\ \mathrm{mm}$. Find normal stress $\sigma$ and strain $\varepsilon$ in the brake cable.

The drag force, $F_{d}$, imposed by the surrounding air on a vehicle moving with velocity V is given by:

$$F_{\mathrm{d}}=C_{\mathrm{d}} \mathrm{A}_{2} \mathrm{pV}^{2}$$

where $C_{d}$ is a constant called the drag coefficient, A is the projected frontal area of the vehicle, and $\rho$ is the air density. Determine the power, in hp, required to overcome aerodynamic drag for an automobile moving at (a) 25 miles per hour, (b) 70 miles per hour. Assume $C_{\mathrm{d}}=0.28, \mathrm{A}=25 \:\mathrm{ft}^{2}$ and $\rho=0.075 \: \mathrm{Ib} / \mathrm{ft}^{2}$