What is the relationship between tire size and pressure changes?

[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.

 

[songoku]

I am sorry for late reply

So what is the total contact area?

I have divided the weight by 4 in my working so I use contact area of one tire, 180 cm²

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

The weight of additional gas is negligible so the force can be considered constant. Since the pressure increases, the are should decrease.

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?
View attachment 351566

Under inflated. The contact area is bigger than tyre with correct pressure.

I don't understand this question

I interpret it as finding the air pressure inside the tire so I think my answer is wrong. Maybe the answer should be atmospheric pressure

Thanks

 

[haruspex]

Maybe the answer should be atmospheric pressure

Do you mean that it should be gauge pressure? If so, probably yes.

What are your answers to c i and c ii now?

 

[songoku]

Do you mean that it should be gauge pressure? If so, probably yes.

Yes, I am sorry. I mean gauge pressure. But since the gauge pressure is not given, we can't answer question (b) in numerical value?

What are your answers to c i and c ii now?

c
(i) decrease
(ii) increase

Thanks

 

[haruspex]

Yes, I am sorry. I mean gauge pressure. But since the gauge pressure is not given, we can't answer question (b) in numerical value?

The gauge pressure is what you calculated, $2.04 \times 10^{5} Pa$. You cannot answer in terms of absolute pressure because you are not given the atmospheric pressure.

c
(i) decrease
(ii) increase

Yes.

 

[songoku]

The gauge pressure is what you calculated, $2.04 \times 10^{5} Pa$. You cannot answer in terms of absolute pressure because you are not given the atmospheric pressure.

Question (b) asks about air pressure inside the tire. Why the answer is not the total pressure of air inside the tire? Can't I take the atmospheric pressure to be just normal, around 1 x 10⁵ Pa?

Thanks

 

[haruspex]

. Why the answer is not the total pressure of air inside the tire?

For the reasons @Lnewqban gave in post #7. There are two standard ways to state a pressure:
- as "gauge", pressure, which means the measure shown by a standard pressure gauge. This shows the excess pressure above atmospheric pressure, because that is what is easy to measure and for most practical purposes is the important statistic. The effective pressure in a tyre is its gauge pressure: that determines how firm it is and whether it is at risk of bursting.
- as absolute pressure. To measure that you need to have on hand a partial vacuum as reference, such as in an aneroid barometer.

School questions ought to state which is being used. If unstated, you have to consider the context. Here, gauge pressure is appropriate. Had the question provided a value for atmospheric pressure then that would have been a hint to answer in absolute.

 

[songoku]

Thank you very much for all the help and explanation Orodruin, haruspex, Lnewqban