Chapter 4.1, Problem 67E

a.

To determine

Determinethe road speed at which the tire is being balanced.

Answer to Problem 67E

The road speed is $\text{35}\text{.7}\text{miles}/\text{hour}$ .

Explanation of Solution

Given:

The moving rate of machine is $480$ revolutions/minute and the diameter of the tire is $25$ inches.

Calculation:

Circumference of the tire $=\pi d=\pi \times 25\text{inches}=25\pi \text{inches}$

Theroad speed $=25\pi \text{inches}\times 480 \text{revolutions}/\text{minute}=37699.11\text{inches}/\text{minute}$

Convert the result in miles/hour.

  $\begin{array}{l}37699.11\text{inches}/\text{minute}\\ \text{=1}\text{.57828}\times {\text{10}}^{-5}\times 37699.11\text{miles}/\text{minute}\\ =0.59499\text{miles}/\text{minute}\\ =0.59499\times 60\text{miles}/\text{hour}\\ \text{=35}\text{.7}\text{miles}/\text{hour}\end{array}$

Hence theroad speed is $\text{35}\text{.7}\text{miles}/\text{hour}$ .

b.

To determine

Find the rate at which the spin balance machine be set for the given speed.

Answer to Problem 67E

The rate is $739.496\text{revolutions/minute}$ .

Explanation of Solution

Given:

The moving rate of machine is $480$ revolutions/minute and the diameter of the tire is $25$ inches. The given speed is $55\text{miles/hour}$ .

Calculation:

Circumference of the tire $=\pi d=\pi \times 25\text{inches}=25\pi \text{inches}$

The road speed $=25\pi \text{inches}\times 480 \text{revolutions}/\text{minute}=37699.11\text{inches}/\text{minute}$

Convert the result in miles/hour.

  $\begin{array}{l}37699.11\text{inches}/\text{minute}\\ \text{=1}\text{.57828}\times {\text{10}}^{-5}\times 37699.11\text{miles}/\text{minute}\\ =0.59499\text{miles}/\text{minute}\\ =0.59499\times 60\text{miles}/\text{hour}\\ \text{=35}\text{.7}\text{miles}/\text{hour}\end{array}$

Let the rate for the given speed $=x\text{revolutions/hour}$ .

Now,

  $\begin{array}{l}\frac{480\times 60\text{revolutions/hour}}{35.7\text{miles/hour}}=\frac{x\text{revolutions/hour}}{55\text{miles/hour}}\\ \Rightarrow x=\frac{480\times 60\times \text{55}}{35.7}\text{revolutions/hour}\end{array}$

  $\begin{array}{l}\Rightarrow x=44369.7478992\text{revolutions/hour}\\ \Rightarrow x=\frac{44369.7478992}{60}\text{revolutions/minute}\\ \Rightarrow x\approx 739.496\text{revolutions/minute}\end{array}$

Hence therateis $739.496\text{revolutions/minute}$ .