Question

Your 1.31×10^3 kg car is supported equally by its four tires, each a inflated to a gauge pressure of 34.1 psi. What is the area of contact each tire makes with the road?

Answer 1

If a force F is exerted over an area A, the pressure P over that area is given by:

`P=(F)/(A)`

The pressure over the area of contact of the tires is the same as the pressure inside the tires. In this case, the force is the weight of the car and the pressure is given. Then, the area of contact is unknown.

Let A be the area of contact of each tire. Then, the total area of contact is 4A and the equation becomes:

`P=(F)/(4A)`

Isolate A from the equation:

`A=(F)/(4P)`

Replace F for the expression mg, which is the weight of the car:

`A=(mg)/(4P)`

Where g is the gravitational acceleration, 9.81m/s^2.

To find the answer, replace the value of each known variable using SI units.

Since 1psi = 6894.76Pa, then:

`A=(\left(1.31*10^3kg\right?\left(9.81(m)/(s^2)\right))/(4\left(34.1psi*(6894.76Pa)/(1psi)\right))=0.0136649...m^2\approx0.0137m^2`

Therefore, the area of contact each tire makes with the road is approximately 0.0137m^2.