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Chapter 6: Q6.1-1PE (page 221)

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?

Short Answer

Expert verified

The odometer should read722.6 km.

Step by step solution

01

Given data

  • The diameter of the wheel is d=1.15m.
  • The number of rotations is 200,000
02

Definition of linear distance

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

03

Calculation of the linear distance

We know that linear distance = angular distance times radius.

Now,

θ=200,000×2π=1.2×106 radianr=d2=1.152=0.575 m

Thus,

s=1.2×106×0.575=722566.3 m=722.6 km

Therefore, the odometer should read722.6 km.

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