Chapter 6, Problem 14RE

a.

To determine

Calculate the angular speed of the engine.

Answer to Problem 14RE

The angular speed of the engine is,

  $w=\text{21991}\text{.15}\frac{rad}{\min }$

Explanation of Solution

Given: The data of the gear ratio is,

  $g=\frac{angular speed of engine}{angular speed of wheels}$

  $\begin{array}{cc}gear& ratio\\ 1& 4.1\\ 2& 3.0\\ 3& 1.6\\ 4& 0.9\\ 5& 0.7\end{array}$

And the frequency of the engine is,

  $f=3500rpm$

Calculation:

The frequency relation is defined as,

  $f=\frac{w}{2\pi }$

Where w is the angular speed of the engine.

Then,

  $w=f\times 2\pi$

  $w=\text{21991}\text{.15}\frac{rad}{\min }$

b.

To determine

Calculate the angular speed of the wheels.

Answer to Problem 14RE

The angular speed of the wheels is,

  $angular speed of wheels=\text{24434}\text{.61}\frac{rad}{\min }$

Explanation of Solution

Given: The data of the gear ratio is,

  $g=\frac{angular speed of engine}{angular speed of wheels}$

  $\begin{array}{cc}gear& ratio\\ 1& 4.1\\ 2& 3.0\\ 3& 1.6\\ 4& 0.9\\ 5& 0.7\end{array}$

And the frequency of the engine is,

  $f=3500rpm$

Calculation:

We know that the gear ratio is defined as,

  $g=\frac{angular speed of engine}{angular speed of wheels}$

Then, if the engine is in the fourth gear,

  $0.9=\frac{\text{21991}\text{.15}}{angular speed of wheels}$

The angular speed of the wheels is,

  $angular speed of wheels=\text{24434}\text{.61}\frac{rad}{\min }$

c.

To determine

Calculate how fast car is travelling.

Answer to Problem 14RE

The solution is,

  $v=\text{36}\text{.46 mi/hr}$

Explanation of Solution

Given: The data of the gear ratio is,

  $g=\frac{angular speed of engine}{angular speed of wheels}$

  $\begin{array}{cc}gear& ratio\\ 1& 4.1\\ 2& 3.0\\ 3& 1.6\\ 4& 0.9\\ 5& 0.7\end{array}$

And the frequency of the engine is,

  $f=3500rpm$

Calculation:

The radius of the wheel is,

  $r=11inch$

Then, the linear speed of the wheel is,

  $v=r\times w$

Then,

  $v=\text{36}\text{.46 mi/hr}$