Total area of contact between tires and ground?

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1. Jan 27, 2015

Dennydont

1. The problem statement, all variables and given/known data
A car has four tires in contact with the ground each of which is inflated to an absolute pressure of 3.1×105Nm^-2. If a person of mass 82 kg gets into the car by how much will the total area of contact between the tyres and the ground increase assuming that the tire pressure remains constant?
m = 82kg
P = 3.1×10^5Nm^-2
g = 9.81ms^-2
P(atmosphere)=10^5Nm^-2

2. Relevant equations
Pressure, P = F/A
F = ma

3. The attempt at a solution
The above equation was used in order to get the solution. P = (9.81ms^-2×82kg)/(3.1x10^5Nm^-2)
= .00259 × 4 (number of tires)
= 0.01m^2

This does not give me the correct answer. Do I have to consider atmospheric pressure? If so, are there any more equations required in this problem?

2. Jan 27, 2015

Staff: Mentor

You need to divide by the number of tires, not multiply. Also, you need to use the gage pressure in the calculation.

Chet

3. Jan 27, 2015

Dennydont

I've used gauge pressure which is 2.1x10^5 and divided by the number of tires instead of multiplying and get 0.021m^2. However, this still isn't the correct answer!

4. Jan 27, 2015

Staff: Mentor

There's something wrong with this result. It is not consistent with your previous calculation. It looks high by a factor of about 10.

Chet

5. Jan 27, 2015

Staff: Mentor

Can you show some details of your calculation? I don't see how you've arrived at 0.021m^2 with the given values and your relevant equation.

6. Jan 27, 2015

Dennydont

You're right, I miscalculated. 9.58cm^2 is what I got but it's only partially correct because this is the change in area per tire, but that's not what I've been asked to find apparently?!

7. Jan 27, 2015

Dennydont

My mistake! What I actually get is 9.58cm^2 but this is the change in area per tire, which is not what I've been asked to find. Very confusing.

8. Jan 27, 2015

Staff: Mentor

Ah...I forgot that. So you neither multiply nor divide by 4 to get the answer.
Chet

9. Jan 27, 2015

Dennydont

So since I don't need to multiply nor divide by 4, and just to be completely sure... Is the answer 38.3cm^2?

10. Jan 27, 2015

Staff: Mentor

Yes, if you did the arithmetic correctly.

Chet

11. Jan 29, 2015

Sam Fielder

To calculate the gauge pressure, is it not the Absolute pressure minus the atmospheric pressure. 3.1x10^5 - 10^5 which would give a negative number?

12. Jan 29, 2015

Staff: Mentor

How do you figure that this gives a negative number?

Chet

13. Jan 29, 2015

Sam Fielder

Well 3.1 - 10 = -6.9 does it not?

14. Jan 29, 2015

Staff: Mentor

You're having a little bit of a notation issue. 3.1x10^5 is supposed to be 310000, and 10^5 is supposed to be 100000. So 310000 - 100000=210000=2.1x10^5.

15. Jan 29, 2015

haruspex

It's 105 = 1 *105 , not 10*105.

16. Jan 29, 2015

Sam Fielder

Yes I realize that now, not sure why it did not click in my head earlier, I should be better at this :p