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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.

Sagot :

The pressure value is given as,

[tex]P=240\text{ kPa}[/tex]

The value of the area is given as

[tex]\begin{gathered} A=190cm^2 \\ A=190\times10^{-4}m^2 \end{gathered}[/tex]

Thus, total area for the four tires is,

[tex]\begin{gathered} A^{\prime}=4\times A \\ A^{\prime}=4\times190\times10^{-4} \\ A^{\prime}=760\times10^{-4}m^2 \end{gathered}[/tex]

The force exerted in terms of pressure and area is,

[tex]\begin{gathered} F=P\times A^{\prime} \\ F=240\times10^3\times760\times10^{-4} \\ F=18240\text{ N} \end{gathered}[/tex]

According to the newton's law,

[tex]F=mg[/tex]

where g is the acceleration due to gravity.

Substituting the known values,

[tex]\begin{gathered} 18240=m\times9.8 \\ m=\frac{18240}{9.8} \\ m=1861.2\text{ kg} \end{gathered}[/tex]

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