Problem 1PE

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 traveled. If the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?

Solution 1PE

Step 1 of 1

The reading ()on the odometer can be found by using the expression for the rotation angle .

=

Now , The wheel goes through 200,000 rotations so,

= 200,000 rot

= rad

The diameter (d) of the wheel is 1.15 m , so the radius of curvature r is r =

r = = 0.575 m

Hence , = r

= ) (0.575)

= 7.226m

= 722.6 km

Therefore , the reading on the odometer is 722.6 km .