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Q6.1-1PE

Expert-verified
Found in: Page 221

College Physics (Urone)

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.

See the step by step solution

Step 1: Given data

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

Step 2: Definition of linear distance

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

Step 3: Calculation of the linear distance

We know that linear distance = angular distance times radius.

Now,

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

Thus,

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

Therefore, the odometer should read 722.6 km.