Tire pressure problem

[Feodalherren]

Homework Statement

Your right rear tire normally has to support a weight of 3000N. The contact area of your tire with the road is 200 square cm. If the pressure in your tire is suddenly reduced from 32 pounds psi to 16 pounds psi, what must be the new contact area to support the car?

Homework Equations

Classical mechanics, pressures in Pascal etc.

The Attempt at a Solution

Not quite sure where to go with this... My intuition tells me that the area should be larger but I'm not sure what equation to start plugging stuff into to prove it.

 

[SteamKing]

What is the relationship between force and pressure?

 

[Feodalherren]

Hmm let's see here.

P=F/A

So the initial pressure is 1500 Pa, correct? How does that help me?

 

[SteamKing]

Read your problem carefully.

In the initial instance, you are given a force, a pressure and an area of contact. Are all of these quantities consistent, when using consistent units?

In the second instance, the pressure in the tire is reduced. Does the force on the tire change? What happens to the contact area when the tire pressure is reduced?

 

[Pkruse]

Back when I used to work heavy equipment, civil engineers would often ask me how much pressure a piece of equipment applied to the ground, so that they could design a concrete slab to park it on. I've seen all sorts of schemes to measure contact area to divide the axle weight by. But that always works out to a number equal to tire pressure. So I would tell them to figure 180 psi because none of the regular equipment is higher than that. Some aircraft is much higher, and that results in some very thick heavily reinforced concrete.

 

[Feodalherren]

Hmm the 3000N remains the same, that's for sure. If the pressure is decreased the contact area must increase... The pressure decreases by 1/2 so the contact area increases by a factor of 2?