Chapter 13.1, Problem 2PP

To determine

To Calculate:The pressure that the car exerts on the ground as it rests on all four tires.

Answer to Problem 2PP

  $1.0\times {10}^2\text{kPa}$

Explanation of Solution

Given data:

Mass, $m=925\text{ kg}$

Length of the rectangle, $l=12\text{ cm }\left(\text{0}\text{.12 m}\right)$

Width of the rectangle, $w=1\text{8 cm }\left(\text{0}\text{.18 m}\right)$

Total number of tires $=4$

Formula used:

A force (per unit area) that acts on any object is defined by pressure. Pressure on any object is calculated by using formula

  $P=\frac{F}{A}$

Where, F = force, m = Mass and A = Area

Area can be obtained as:

  $A=l\times w$

Here, force exerted on the tires is equal to the weight of the car.

  $F=m_{car}g$

Where, $g=9.80{\text{m/s}}^{\text{2}}$ is the gravitational acceleration.

Calculation:

Use the formula of pressure:

  $P=\frac{m_{car}g}{A}$

Now, substitute the given values in the above formula:

  $\begin{array}{c}P=\frac{\left(\text{925}\text{kg}\right)\left(\text{9}\text{.80}{\text{m/s}}^{\text{2}}\right)}{\left(\text{4}\right)\left(\text{0}\text{.12}\text{m}\right)\left(\text{0}\text{.18}\text{m}\right)}\\ =1.0\times {10}^2\text{kPa}\end{array}$

Conclusion:

The pressure that the car exerts on the ground as it rests on all four tires is $1.0\times {10}^2\text{kPa}$ .