The four tires of an automobile are inflated to a gauge pressure of 1.7 10^{5} Pa. Each tire has an area of 0.020 m^{2} in contact with the ground. Determine the weight of the automobile.

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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 :)

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