# The weight of your 1400 kg car is supported equally by its four tires, each inflated to a gauge pressure of 35.0 lb/in^2. What is the area of contact each tire makes with the road? (answer must be in cm^2) What gauge pressure is required to give an area of contact of 125 cm^2 for each tire? (answer must be in lb/in^2)

The weight of your 1400 kg car is supported equally by its four tires, each inflated to a gauge pressure of 35.0 $lb/i{n}^{2}.$
What is the area of contact each tire makes with the road? (answer must be in $c{m}^{2}$) What gauge pressure is required to give an area of contact of $125c{m}^{2}$ for each tire? (answer must be in $lb/i{n}^{2}$)
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Jimena Torres
Given
$W=1400×9.8=13720N$
gauge pressure $=35.0lb/i{n}^{2}.$
in Pa =$35×6875Pa=\phantom{\rule{0ex}{0ex}}P=241.325Pa=241325P$a
Force on each type $F=\frac{13720}{4}=3430N$
$P=\frac{F}{A}$
Hence area of Contact
$A=\frac{F}{P}=\frac{3430}{241325}=0.014213{m}^{2}$
$A=1.4213×{10}^{2}c{m}^{2}\phantom{\rule{0ex}{0ex}}A=142.13c{m}^{2}$
b) If $A=125c{m}^{2}=0.0125{m}^{2}\phantom{\rule{0ex}{0ex}}P=\frac{F}{A}=\frac{3430}{0.0125}=274400Pa\phantom{\rule{0ex}{0ex}}P=\frac{274410}{6895}=39.797lb/i{n}^{2}$