Gauge Pressure of Tires - find car mass

[BeiW]

Gauge Pressure of Tires -- find car mass

Homework Statement

The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 22.0 cm-squared, estimate mass of the car.

P=240 kPa
A=22.0 cm-squared
g=9.8 m/s^2

Homework Equations

P=F/A
1 atm = 1.013x(10^5) N/m^2 = 101.3 kPa
A=.22 m^2 for each tire

The Attempt at a Solution

P = 2.4x(10^5) N/m^s = F/A = (mg)/A for each tire
m= (PA)/g = (2.4x(10^5))(.22) / (9.8) = 5387.76 kg?

 

[rock.freak667]

1cm = 10^-2m -> 1cm²=10^-4m².

You need to convert 22cm^2 to m^2, I think you will also need multiply by 4 since there are 4 tires.

 

[BeiW]

So the tire area is .0022m²?
Then for 4 tires, the area is .0088m².

m= (PA)/g = (2.4 x 10⁵)(.0088) / (9.8) = 215.510 kg
If you round that, it should be 2.2 x 10² kg, but the real answer is 2.2 x 10³...

What am I missing?

1cm = 10^-2m -> 1cm²=10^-4m².

You need to convert 22cm^2 to m^2, I think you will also need multiply by 4 since there are 4 tires.

 

[gneill]

So the tire area is .0022m²?
Then for 4 tires, the area is .0088m².

m= (PA)/g = (2.4 x 10⁵)(.0088) / (9.8) = 215.510 kg
If you round that, it should be 2.2 x 10² kg, but the real answer is 2.2 x 10³...

What am I missing?

There is probably a typo in the "footprint" area. Things would look more realistic if the value was 220cm².

 

[BeiW]

There is probably a typo in the "footprint" area. Things would look more realistic if the value was 220cm².

I just checked the book again, and you're right. It actually says 220cm.

Thanks! :)