Chapter 20, Problem 59A

An automobile is supported by four tires inflated to a gauge pressure of 180 kPa. The area of contact of each of the tires (ignoring the effects of tread thickness) is $190c{m}^2$ (which means the total area of tire contact is $0.076m^2$

). Estimate the mass of the car in kilograms.

To determine

The mass of the car .

Answer to Problem 59A

The mass of the car is $1396\text{kg}$

Explanation of Solution

Given:

Gauge pressure of each tires = 180Pa

Total area of tire contact = 0.076 m²

Formula used:

In order to support an automobile which is lying on the road, it's weight should be balanced by the force exerted by the gauge pressure. Mathematically, it is expressed as,

  $mg=P_{\text{gauge}}A$

Here, $m$ is mass of the automobile, $g$ is acceleration due to gravity, $P_{g\text{supe}}$ is gauge pressure, and

  $A$ is the total area of contact of all tires.

Calculation:

Substitute $1.80\times {10}^5\text{Pa}$ for $P_{{\text{gam}}_8\text{r}},0.076{\text{m}}^2$ , for $\text{A},$ , and $9.8\text{m}/{\text{s}}^2$ for $g$ to solve for mass of the car.

  $\begin{array}{c}m\left(9.8\text{m}/{\text{s}}^2\right)=\left(1.80\times {10}^5\text{Pa}\right)\left(0.076{\text{m}}^2\right)\\ =1395.9\\ \approx 1396\text{kg}\end{array}$

Conclusion:

Therefore, the mass of the car is $1396\text{kg}$