Pressure of car tires

[songoku]

Homework Statement

A car of weight 1500 kg has four tires, each of which has an area of 180 cm[SUP]2[/SUP] in contact with the road.
a) Calculate the pressure under each tire (in Pa).

b) State the pressure of the air inside the tire.

c) If the driver puts more air into the tire, what will happen to:
(i) the area in contact with the ground
(ii) the pressure on the road

Relevant Equations

P = F / A

a) $P=\frac{F}{A}=\frac{\frac{1500\times 9.8}{4}}{180\times 10^{-4}}=2.04 \times 10^{5} Pa$

b) Is the pressure in (a) gauge pressure? My answer for (b) is 2.04 x 10 ⁵ + Po where Po is atmospheric pressure

c)
(i) it will increase since the size of the tire also increases

(ii) I am not sure about this one. The area increases but the force exerted by the tire also increases due to increase in number of air molecules inside the tire but I suppose maybe the increase in force is smaller compared to increase in area so my answer will be the pressure decreases.

Is my answer correct? Thanks

 

[Orodruin]

a) How many tires?

c) No. How does the force change? What does it mean for the computation in (a)?

 

[songoku]

a) How many tires?

4

c) No. How does the force change? What does it mean for the computation in (a)?

I would say the force increases since more air is in the tire so the weight of the air increases.

I am not sure what it means for computation in (a). The force increases, the pressure also increases, not sure about the area

Thanks

 

[haruspex]

I would say the force increases since more air is in the tire so the weight of the air increases.

Compared to the weight of the car, you can take that as negligible.

 

[Orodruin]

4

So what is the total contact area?

I would say the force increases since more air is in the tire so the weight of the air increases.

Compared to the weight of the car, which is the main load?

 

[Orodruin]

For a bit of intuition: Would you say this tyre is over or under inflated? What about the contact area in comparison to a tyre with correct pressure?

 

[Lnewqban]

b) State the pressure of the air inside the tire.

I don't understand this question.

b) Is the pressure in (a) gauge pressure? My answer for (b) is 2.04 x 10 5 + Po where Po is atmospheric pressure

The practical way to measure internal air pressure in any tire is via a manometer; therefore, the measured value is not of absolute pressure, but above the atmospheric pressure.

When not connected to an inflated tire, all manometers or tire gauges should be showing 0 (respect to the actual surrounding atmospheric pressure).

Also, the external force of the contact patch on the road will not change for any internal force of the air on the interior surface of the tire.
Both are pretty much independent from each other.