Calculating the tire pressure

[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.

 

[thomate1]

Based on the given information, I would explain to my friend that the tire pressure can be estimated using the formula P=F/A, where P is the tire pressure, F is the force exerted on the tire (which we know is 1/4 of the car's weight), and A is the area of the flattened segment of the tire in contact with the road.

Since we know that the flattened segment is 13cm long and 15cm wide, we can calculate the area by multiplying the length and width, which gives us 195cm^2. However, this is not the true area of the tire in contact with the road, as there is also the sidewall height to consider. Without knowing the sidewall height, it would be difficult to accurately calculate the tire pressure.

I would also mention that the density of the tire (which is the mass of the tire divided by its volume) does not directly affect the tire pressure. It is more relevant for determining the load capacity of the tire.

In this situation, it would be best to find a tire gauge to get an accurate measurement of the tire pressure. Alternatively, we could also take the car to a mechanic or gas station to have the tire pressure checked.