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Q6.1-1PE

Expert-verifiedFound in: Page 221

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance travelled. If the wheel has a 1.15 m** **diameter and goes through 200,000** **rotations, how many kilometres should the odometer read?**

The odometer should read** **722.6 km.

- The diameter of the wheel is $d=1.15\mathrm{m}$.
- The number of rotations is 200,000

**Linear distance is the distance covered straight from a point to the concerned point.**

We know that linear distance = angular distance times radius.

Now,

$\begin{array}{c}\theta =200,000\times 2\pi \\ =1.2\times {10}^{6}\text{\hspace{0.33em}radian}\\ r=\frac{d}{2}\\ =\frac{1.15}{2}\\ =0.575\text{\hspace{0.33em}m}\end{array}$Thus,

$\begin{array}{c}s=1.2\times {10}^{6}\times 0.575\\ =722566.3\text{\hspace{0.33em}}\text{m}\\ =722.6\text{\hspace{0.33em}km}\end{array}$

Therefore, the odometer should read** 722.6 km**.** **

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