How Do You Calculate Tire Pressure Without a Gauge?

[Jeff231]

Homework Statement

"A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. From the owner's manual you find the car's mass is 1500kg. It seems resonable to assume that each tire supports one-fourth of the weight. With a ruler you find that the tires are 15cm wide and the flattened segment of the tire in contact with the road is 13cm long. What answer do you give your friend?"

Homework Equations

P = Po + (density)gd d=depth
P= F/A
density(rho) = m/v

The Attempt at a Solution

I know the force is 1/4(9.8)(1500).
I know Po is just the outside pressure (constant).

I'm confused on how density plays in the this equation/question. Also the area, A I'm confused how it's possible to find the area of the tire with just knowing how wide the tire is, how much ground is touching the tire, without knowing the sidewall height. It's not like the whole thing is made of tire, unless I'm suppose to assume there's no wheel?

Thanks.

 

[mgb_phys]

You don't need to know the volume of the tire, just the change in volume due to the weight of the car - assume the tire would be round if the weigth of thecar was removed.