Gauge pressure needed to lift a car with a hydraulic piston

[sghaussi]

Hello! I was wondering if you could help me with a homework problem:

The piston of a hydraulic automobile lift is X meters in diameter.

What gauge pressure, in pascals, is required to lift a car with a mass of Y kg?

I know that a piston is a cylindrical shaped apparatus - however I believe that does not affect my calculations.

I also know this about pressure: p = F/A

F = mass x a so in my case that would be: Y kg x 9.8m/s

A (of a circle) = 2 x pi x r^2 r being half my diameter so X/2


From using this formula, the pressure is calculated in Pascals. The answer I get however is wrong. Am i using the wrong formula? should find the volume of the piston? I'm not sure how that would help... hope someone can give me some hints! =)

 

[whozum]

If you are considering the pressure on just the bottom of the piston (or top) then you only need to consider the area of one circle, not two.

 

[sghaussi]

that's right, i should only consider the area of one circle. that "2" in front of pi r squared was a typo... =) I've been trying to calculate it assuming it's one circle but I'm doing something wrong. =/

 

[whozum]

Is your final result

$$\frac{4(Y kg)(9.8 m/s^2)}{\pi x^2}$$?

 

[sghaussi]

Why is the equation being multiplied by 4?

 

[whozum]

The 4 comes from the denominator, since you are squaring X/2, you get x^2/4, and instead of having stacked fractions, you can multiply top and bottom by 4 to get what I gave.

 

[sghaussi]

My final equation looks like this:


(Y kg)*(9.8 m/s^2) / (pi)*(r^2) = p (pascals)

 

[sghaussi]

regarding the equation that I am using (p = F/A), does that even look like the correct equation I need to solve this type of problem?

 

[whozum]

Express it in terms of x and y, I think that's what you need to do. Is this online homework? Is that the complete problem?

 

[OlderDan]

regarding the equation that I am using (p = F/A), does that even look like the correct equation I need to solve this type of problem?

Yes it is the right equation. Your first calculation of area was wrong. If you get the area right, I think you will have it.

 

[sghaussi]

yes, it is online homework and that is the complete problem except "x" and "y" there are real numbers. so instead of multiplying by 4 i just divided x by two before I plugged it into the equation.

 

[whozum]

Did you divide correctly? ;)
Lets see the numbers.

 

[sghaussi]

got it.. i WAS getting the area wrong.. i was imputing it incorrectly into the calc. thanks so much for your time and patience!