Aamc 7 ps #47

[RUc10]

---

Members don't see this ad.

Should be a simple answer. Question was:

What is the difference in pressure between 2 points given they are separated by a vertical difference of .25m in a tank of water? (Density of water 1,000 kg/m^3 and g = 10 m/s^2)

Answer is C) 2500 N/m^2


I got this correct but I guessed and moved on it wasn't making sense. I know the formula for pressure difference as rho x g x y and that the units of pressure are N/m^2. It's helped a lot in improving my score to focus on making sure units are correct before I choose my final answer. However, unless I am making a dumb mistake or there is some shortcut the the units of pressure I didn't review, it would seem that the units when you multiply the 3 given values come out to kg/ms^2.

How do the units for the problem match up? I feel like it's something simple and I'm gonna feel slow hearing the explanation 😳

 

[GRod18]

Should be a simple answer. Question was:

What is the difference in pressure between 2 points given they are separated by a vertical difference of .25m in a tank of water? (Density of water 1,000 kg/m^3 and g = 10 m/s^2)

Answer is C) 2500 N/m^2


I got this correct but I guessed and moved on it wasn't making sense. I know the formula for pressure difference as rho x g x y and that the units of pressure are N/m^2. It's helped a lot in improving my score to focus on making sure units are correct before I choose my final answer. However, unless I am making a dumb mistake or there is some shortcut the the units of pressure I didn't review, it would seem that the units when you multiply the 3 given values come out to kg/ms^2.

How do the units for the problem match up? I feel like it's something simple and I'm gonna feel slow hearing the explanation 😳

well you know that pressure = Force / Area = Pascal = N/m^2

So with Roh x g x h you would get kg/m^3 x m/S^2 x m so if you write it all down you'd get kg x m^2 / m^3 x S^2 You know that Kg x m/S^2 is same thing as 1 N. and if you cross out 1 meter on top and bottom you'll have m^2 left on the bottom. So your final answer is kg x m/s^2 x m^2

write down what I typed on paper, and you should see it. You can always derive units from formulas, if you know that F = ma you can derive Newton units, and if you know force/area you can find pressure units.

 

[vsl5]

P = rho * g * h

in units

P (Pa = N/m^2) = (kg/m^3) * 10m/s^2 *m
= (kg/(m s^2)


1 N = kgm/s^2 , so 1 Pa = 1kgm/s^2 /m^2 = 1kg/ms^2 which is the same as the right side

 

[RUc10]

Thanks to the both of you. GRod your explanation helped me realize where I was going wrong. I was going too far with my unit analysis. It helps a lot to take out a Newton or the equivalent of N (kg * m/s^2) and then cancel out the rest of the remaining units.

I was canceling everything out and ending up with kg/ms^2 wondering what the hell was going on. In retrospect N/m^2 actually is the same thing as kg/ms^2 just written a different way. Bleh, wasted all that time on an easy question.

Thanks again.