A simple Fluid Dynamics/Pressure HW question

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In a hydraulic press problem, a small piston with a cross-sectional area of 3.63 cm and a larger piston with an area of 50.7 cm are used to balance a 41.8 kN force on the larger piston. The relationship between pressure and force is established using the equation P=F/A. The user attempts to calculate the force on the small piston but initially uses diameters instead of areas, leading to an incorrect result. After realizing the mistake, the importance of careful reading and attention to detail in problem-solving is emphasized. Accurate calculations are crucial for determining the correct force needed on the small piston.
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Homework Statement


A piston of cross-sectional area a is used in a hydraulic press to exert a small force of magnitude f on the enclosed liquid. A connecting pipe leads to a larger piston of cross-sectional area A (the figure). If the piston diameters are 3.63 cm and 50.7 cm, what force magnitude on the small piston will balance a 41.8 kN force on the large piston?

Homework Equations


P=F/A

The Attempt at a Solution


So I'm pretty sure I'm doing this right especially since we did a similar one in class so I think it might just be a math error here's what I did.

For the smaller side Ps = Fs/as

For the larger side Pb = Fb/Ab

Ps = Pb

Fs/as = Fb/Ab

Solve for Fs
Fs = Fb/Ab * as

Plug in values (Fb 41.8kN = 41800N) (Ab 50.7cm =.507m) (as 3.63cm = .0363m)

Fs = (41800/.507)*.0363 = 2992.78N WileyPlus says its wrong though, so did I make a mistake?
 

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For some reason you plugged in the diameters instead of the areas.
 
paisiello2 said:
For some reason you plugged in the diameters instead of the areas.
I guess I did. I didn't even notice it said diameters thanks. I must remember to read more thoroughly next time.
 

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