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Question

Help... answer this What’s the formula I need to use? A 78 N force is applied to a 0.15 m2 surface that is connected by a fluid to another surface that has an area of 50.00 m2. What force does the larger surface exert?

Answer 1

By Pascal's principle, the application of a force F₁ on an area A₁ causes the pressure to rise everywhere in the fluid by F₁/A₁.  On the other area A₂, the pressure rise must be the same, so there will be a force F₂ on A₂ such that

 

F₂/A₂ = F₁/A₁

 

F₂ = (A₂/A₁)F₁

 

If A₂ > A₁, the output force at A₂ will be greater than the input force F₁.  This is how a hydraulic lift generates a large output force given a small input force.

 

F₁ = 78 N

A₁ = 0.15 m²

A₂ = 50.00 m²

 

F₂ = (A₂/A₁)F₁ = (50.00/0.15)(78) N = 26,000 N

 

You can see that F₂ is much larger than F₁, even though the pressures are the same at both ends.  That is due to the second area being so much larger that the first area.