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Car's tire pressure calculation

PostPosted: Tue 12 April, 2011 17:35
by Integr88
Your car weighs (from the manual) 1550kg and the manual of your car recommends 30psi pressure.
With the ruler you find that the tires are 16 cm wide and the flattened segment of the tire in contact with the road is 14 cm long.
what are the pressures of the tire the tire?

Re: Car's tire pressure calculation

PostPosted: Tue 12 April, 2011 17:55
by Galaxy
we know that car has 4 tires. so the total weight has been distributed to each tire.
lets find how much pressure has been applied to each tire.

each tire has 16x14=224`cm^2` area.
so the pressure on one tire is `1/4` of the whole weight of the car so `1550/4=387.5kg`
we can see that we have 387.5kg per 224`cm^2` area of tire or `(387.5kg)/(224cm^2)`

Now we have to convert it to PSI (pounds per inch square).
because 224 is squared of a value so we have to take the root of it `sqrt224=14.96cm` now from conversion unit we know 1cm=0.3937in
so `14.96*0.3937=5.892in` so we have to square it to get the area `5.892^2=34.72\i\n^2`

from our original equation `(387.5kg)/(224cm^2)` we converted ` 224cm^2`to be 34.72 inch squared.
Now convert to 387.5kg to pounds so multiply it by 2.2 to get lb. (2.2)*387.5=854.29lb.

ok the pressure is `(854.29lb)/(34.72\i\n^2)=24.6`psi.

24.6psi is the pressure of the tire.