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.

 N
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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