Question

The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 190 cm2 (area touching the ground), estimate the mass of the car. No units on answer.

Answer 1

The pressure value is given as,

`P=240\text{ kPa}`

The value of the area is given as

`\begin{gathered} A=190cm^2 \\ A=190*10^(-4)m^2 \end{gathered}`

Thus, total area for the four tires is,

`\begin{gathered} A^(\prime)=4* A \\ A^(\prime)=4*190*10^(-4) \\ A^(\prime)=760*10^(-4)m^2 \end{gathered}`

The force exerted in terms of pressure and area is,

`\begin{gathered} F=P* A^(\prime) \\ F=240*10^3*760*10^(-4) \\ F=18240\text{ N} \end{gathered}`

According to the newton's law,

`F=mg`

where g is the acceleration due to gravity.

Substituting the known values,

`\begin{gathered} 18240=m*9.8 \\ m=(18240)/(9.8) \\ m=1861.2\text{ kg} \end{gathered}`

Thus, the value of the mass of the car is 1861.2.