How Do You Calculate Tire Contact Area Using Pascal's Law?

[joe98]

Pascals Law Problem

Homework Statement

You have a vehicle with four tires of 20 cm wide with 2 atm air pressure. Calculate
contact area (cm^2) of each tire on the road. The gross vehicle weight is 1 tonne.

Homework Equations

P=F/A
P=ρgh

The Attempt at a Solution

F=mg=1x10^6x9.8=9.8x10^6

A=F/P
therefore, A=(9.8x10^6)/200000=49m^2

I am not sure if I am right so far,

can u assist me if I am incorreect

cheers

 

[joe98]

Is this method of calculation correct?

 

[gneill]

Homework Statement

You have a vehicle with four tires of 20 cm wide with 2 atm air pressure. Calculate
contact area (cm^2) of each tire on the road. The gross vehicle weight is 1 tonne.

Homework Equations

P=F/A
P=ρgh

The Attempt at a Solution

F=mg=1x10^6x9.8=9.8x10^6

That's a lot of kilograms for a tonne! tonne = 10³ kg.

A=F/P
therefore, A=(9.8x10^6)/200000=49m^2

The method is okay for finding the total contact area. Just fix the tonne value.

 

[joe98]

ooh thnx gneil much appreciated

 

[asteriatic]

Hi there,

It looks like you are on the right track with your solution. Let's break it down further:

F=mg=1x10^6x9.8=9.8x10^6

This is correct, you have calculated the weight of the vehicle (1 tonne = 1x10^6 grams) and multiplied it by the acceleration due to gravity (9.8 m/s^2) to find the force exerted by the vehicle on each tire.

Now, we can use P=F/A to find the pressure exerted by the vehicle on each tire. You have correctly identified that the pressure (P) is equal to the force (F) divided by the contact area (A). However, in your solution, you have used a pressure of 2 atm, which is given in the problem. Therefore, the correct equation to use would be:

P=F/A

2 atm = (9.8x10^6 g x 9.8 m/s^2)/A

We can simplify this equation by converting grams to kilograms (1 g = 0.001 kg) and rearranging to solve for A:

2 atm = (9.8x10^6 kg x 9.8 m/s^2)/A

A = (9.8x10^6 kg x 9.8 m/s^2)/(2 atm)

A = 4.9x10^6 kg x m/s^2

A = 4.9x10^6 N

This gives us the total contact area for all four tires. To find the contact area for each individual tire, we can divide this value by 4:

A = 4.9x10^6 N/4 = 1.225x10^6 N

Therefore, the contact area for each tire is 1.225x10^6 N or 49 cm^2.

I hope this helps! Let me know if you have any further questions.