- #1
Nghi
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Homework Statement
The weight of your 1205 kg car is supported equally by its four tires, each inflated to a gauge pressure of 35.7 lb/in.^2.
a) What is the area of contact each tire makes with the road? (in m^2)
b) What gauge pressure is required to give an area of contact of 113 cm^2 for each tire? (in lb/in^2)
Homework Equations
Pgauge = P - Patmosphere
Pressure = Force/Area
The Attempt at a Solution
I actually went to my professor for help on this one, hehe. He told me that since the weight is equally supported, I just had to make sure that the force is divided by four. So I did that. First I found the real 'P'.
35.7 = P - 14.7
P = 50.4 lb/in^2
Since they wanted the area of contact in meters, I decided to convert the pressure into N/m^2.
50.4 lb/in^2 x (1.01e5 N/m^2 / 14.7 lb/in^2) = 346285.7143 N/m^2 (we're going to let that equal to X to make it simpler)
Now that I had the pressure and the force, all I should do is plug it into the definition of pressure.
P = F/A
X = (1205 x 9.81 / 4) / A
A = 2955.2625 / X
A = 0.00853 m^2
This isn't the answer, though, and I'm confused as heck. This was how my professor explained it to me, and it's wrong. o_o
For part b, I should theoretically just work backwards. First, I convert cm^2 to m^2.
113 cm^2 x (1 m^2/10000 cm^2) = 0.0113 m^2
P = F/A
P = 2955.2625/0.0113
P = 261527.6549 N/m^2 x (14.7 lb/in^2 / 1.01e5 N/m^2) = 38.064 lb/in^2
Pgauge = P - Patmosphere
Pgauge = 38.064 - 14.7
Pgauge = 23.364 lb/in^2
This is also the wrong answer. :/
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