Pressure question: Weight of a car calculated from tyre contact patch area

[shirozack]

Homework Statement

Each tyre of a car exerts a pressure of 5N/cm2 . the area of each tyre in contact with the ground is 10cm2. what is the weight of the car?

Relevant Equations

P=F/A

I tried 2 ways to solve it but both yielded different answers. i would like to know which is correct and why the other is wrong. thank you.

method 1: consider force of each tyre. 5 x 10 = F = 50N. so 4 tyres = 200N = weight

method 2: consider the whole car, total pressure = 4x5 = 20. total area = 4x10 = 40. so total weight = P x A = 20 x 40 = 800N.

 

[haruspex]

total pressure = 4x5 = 20
[/QUOTE]
Using what rule or physical principle?

 

[shirozack]

idk, is it wrong?
or is pressure across one wheel = pressure across the whole car? why? what principle is this? pascal's law?
so total pressure = total Force (weight) / total area
pressure across 1 wheel = weight / 4 x 10
5 x 40 = weight = 200 N ?

 

[haruspex]

idk, is it wrong?
or is pressure across one wheel = pressure across the whole car? why? what principle is this? pascal's law?
so total pressure = total Force (weight) / total area
pressure across 1 wheel = weight / 4 x 10
5 x 40 = weight = 200 N ?

What happens if you consider the $10cm^2$ of one tyre's footprint as composed of ten $1cm^2$ areas side by side? The pressure above each is still $5N/cm^2$. Does that add up to $50N/cm^2$?

Pressure is force per unit area. Bringing in additional tyres increases the total force but also increases the total area. What you did was like saying that ten cars moving at 30kph equates to one moving at 300kph.