The four tires of an automobile are inflated to a gauge pressure of 1.7 105 Pa.

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The four tires of an automobile are inflated to a gauge pressure of 1.7  105 Pa. Each tire has an area of 0.020 m2 in contact with the ground. Determine the weight of the automobile.

Jun 11th, 2015

Thank you for the opportunity to help you with your question!

So first, we use this expression:

P = F/A ;  where: P is the pressure (in Pa) , F is the force (in N), and A is the area (in m^2).

So the total area would be the area of a tire in contact with the ground times 4 (since we have 4 tires). Then we have:

A = 4(0.020 m^2) = 0.08 m^2

Then we solve for F from the above expression like this:

P = F/A  ------------>  A*P = A*F/A  ------------->  A*P = F

So the force F is the one exerted by the weight of the automobile. This means that F = W (where W is the weight of the automobile). So finally, we have:

F = A*P  --------->  W = A*P

Then we just enter 1.7 10^5 Pa in place of P and 0.08 m^2 in place of A. Let's remember a Pascal is Newton /m^2. So we have:

W = (0.08 m^2)(1.7 10^5 Pa) = (0.08 m^2)(1.7 10^5 N/m^2) = 13600 N

So the weight of the automobile is 13600 N.

I hope that this will help you. Please let me know if you have any doubt or question :)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 11th, 2015

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