Chapter 5, Problem 9P

* EST A tire-pressure monitoring system warns you with a dashboard alert when one of your car tires is significantly underinflated, possibly creating unsafe driving conditions. How does the car know when to turn on the alert? Many cars have sensors that measure the period of rotation of each wheel. Based on the period, the car's computer determines the relative size of the tires when the car is moving at a certain speed. (a) Explain how the period of the wheel rotation is related to the size of the tire. (b) Derive a mathematical equation that relates the period T of the wheel rotation to the tire radius r and the speed v of the car. (c) Figure P5.9 shows a properly inflated tire (left) and an underinflated tire (right) of the same car. Estimate the percent change of the period of the underinflated tire compared to the properly inflated tire. (d) Estimate the distance this car would have to travel for the difference between the numbers of turns of the two wheels to be equal to one turn. Which will undergo more turns, the underinflated or the properly inflated tire?