Weight = Pressure * Total Area

AI Thread Summary
The discussion focuses on calculating the mass of a car using the gauge pressure in its tires and their footprint area. Each tire has a gauge pressure of 240 kPa and a footprint of 220 cm², leading to a total area of 880 cm² for all four tires. The correct approach involves using the pressure formula, where total weight equals pressure multiplied by total area, without adding atmospheric pressure. Participants clarify that the pressure should only be used once and emphasize the importance of treating each tire's pressure consistently. Ultimately, the calculation leads to the conclusion that the mass of the car can be derived directly from the given values.
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The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 220 cm2, estimate the mass of the car.

@Mods: please move if this is too easy for this forum.
 
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#H34N1 said:
The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 220 cm2, estimate the mass of the car.

@Mods: please move if this is too easy for this forum.

Hi #H34N1! Welcome to PF! :smile:

Show us how far you've got, and where you're stuck, and then we'll know how to help you! (same for your other thread, of course) :smile:
 
[hide=My work]Pressure = F/A.

There are four tires and four footprints so the total pressure of all four tires is 240*4+101.3 = 1061.3.

I am not sure if I need to add the atmospheric pressure to the gauge pressure. There could be reasons for both. Adding atmospheric pressure is correct because it is the pressure against which the tire is inflated. On the other hand, the atmospheric pressure also adds to the mass of the car so I am not sure how to proceed here.

The total area is 220*4 = 880cm^2. We now have to convert to m^2 because the initial footprint is given in terms of cm^2 and the pressure is given in kPa. $=0.088$.F = mg, so we have

1061.3 = mg/0.088

Solving for m, we have m=9.53004082 kg, which does not seem right.
 
You can not add pressure in this case.
 
pixel01 said:
You can not add pressure in this case.

Hi H34N1! :smile:

Yes, pixel01 is right:

pressure = total mass / total area.

You must only use the pressure once! :smile:
 
tiny-tim said:
You must only use the pressure once! :smile:

hmm … on second thoughts, although that statement is correct, it only works because all the tyres have the same pressure (which they need not), and so in the general case you should consider each tyre separately.

The amount of weight supported by each tyre (equal to the reaction force on that tyre from the ground) divided by the contact area for that tyre equals the pressure for that tyre:

W1 = P1A1 etc

In this case, the Ps are all the same.

So total weight = W1 + W2 + W3 + W4 = P(A1 + A2 + A3 + A4) :smile:
 

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