Chapter 4.1, Problem 44E

Solution

(a)

To calculate : The speed of each vehicle in mph when the wheels are turning at $800\text{ rpm}$ .

The speed of Chevy Spark EV, Nissan Leaf SL, and Tesla S in mph is $54.71$ , $60.66$ , and $65.89$ respectively.

Given information :

The table showing the size specifications for the tires that come as standard equipment on three 2017 all-electric vehicles.

Vehicle	Tyre Type	Tyre Diameter (inches)
Chevy Spark EV	$188/55-15$	$23.0$
Nissan Leaf SL	$215/50-17$	$25.5$
Tesla S	$245/45-19$	$27.7$

Formula used:

To convert revolution per minute to miles per hour, the formula used is:

  $\frac{\text{Revolution per radian}\times \text{Radius}}{12\times 5280}$

Calculation :

To find the speed of each vehicle in mph, convert revolution per minute to miles per hour.

	Chevy Spark EV	Nissan Leaf SL	Tesla S
Tyre Diameter (inches)	$23.0$	$25.5$	$27.7$
Tyre Radius (inches)	$11.5$	$12.75$	$13.85$
Revolution per minute	$800$	$800$	$800$
Revolution per hour	$800\times 60=48000$	$800\times 60=48000$	$800\times 60=48000$
Radian per revolution	$2\pi$	$2\pi$	$2\pi$
Revolution per radian	$301440$	$301440$	$301440$
Inches per feet	$12$	$12$	$12$
Feet per mile	$5280$	$5280$	$5280$
Speed in mph	$\begin{array}{l}\frac{301440\times 11.5}{12\times 5280}\\ \approx 54.71\end{array}$	$\begin{array}{l}\frac{301440\times 12.75}{12\times 5280}\\ \approx 60.66\end{array}$	$\begin{array}{l}\frac{301440\times 13.85}{12\times 5280}\\ \approx 65.89\end{array}$

Therefore, the speed of Chevy Spark EV, Nissan Leaf SL, and Tesla S in mph is $54.71$ , $60.66$ , and $65.89$ respectively.

(b)

To calculate : The number of more revolutions that the tire of the Leaf shall make in order to travel a mile as compared to the Tesla.

The number of more revolutions that the tire of the Leaf shall make in order to travel a mile as compared to the Tesla is $64$ .

Given information :

The table showing the size specifications for the tires that come as standard equipment on three 2017 all-electric vehicles.

Vehicle	Tyre Type	Tyre Diameter (inches)
Chevy Spark EV	$188/55-15$	$23.0$
Nissan Leaf SL	$215/50-17$	$25.5$
Tesla S	$245/45-19$	$27.7$

Calculation :

Nissan Leaf SL travels $60.66$ miles in an hour.

So, the time taken to travel one mile is,

  $\begin{array}{l}=\frac{60}{60.66}\\ =0.99\end{array}$ .

Its wheels revolves $800$ revolutions per minute.

Number of revolution required for a mile will be,

  $\begin{array}{l}=0.99\times 800\\ =792\end{array}$

Tesla S travels $65.89$ miles in an hour.

So, the time taken to travel one mile is,

  $\begin{array}{l}=\frac{60}{65.89}\\ =0.91\end{array}$ .

Its wheels revolves $800$ revolutions per minute.

Number of revolution required for a mile will be,

  $\begin{array}{l}=0.91\times 800\\ =728\end{array}$

Therefore, the number of more revolutions that the tire of the Leaf shall make in order to travel a mile as compared to the Tesla is,

  $\begin{array}{l}=792-728\\ =64\end{array}$

(c)

To explain : The effect on the odometer (which measures mileage) and speedometer readings if a 2017 Nissan Leaf were equipped with the Tesla’s $27.7\text{ in}$ tires.

The speedometer and the odometer readings will increase.

Given information :

The table showing the size specifications for the tires that come as standard equipment on three 2017 all-electric vehicles.

Vehicle	Tyre Type	Tyre Diameter (inches)
Chevy Spark EV	$188/55-15$	$23.0$
Nissan Leaf SL	$215/50-17$	$25.5$
Tesla S	$245/45-19$	$27.7$

Explanation :

If a 2017 Nissan Leaf were equipped with the Tesla’s $27.7\text{ in}$ tires, then the number of revolutions per mile will be reduced. This will result in the increase in the readings of the speedometer by the number of revolutions reduced and the odometer readings will also increase as the mileage will improve as the number of revolutions will be reduced as compared to earlier to cover the same distance.