Two pistons push down on the fluid filling two cylinders connected by a narrow hose, as shown in the figure. The area A ₁ is 1 square inch, and the area A₂ is 10 square inches. A force of 4 pounds is exerted downward on piston 1, as shown. The pressure on A ₂ in psi is A) 0.25. B) 0.4. C) 4. D) 10. E) 40.

Question

Quizplus · Accepted Answer

Pressure = Force/Area
The force exerted on piston 1 is 4 pounds. The area of piston 1 is 1 square inch, so the pressure on piston 1 is 4 pounds per square inch (psi). 
Since the fluid is incompressible, the pressure on piston 2 must also be 4 psi. 
The area of piston 2 is 10 square inches, so the force on piston 2 is (pressure on piston 2) x (area of piston 2) = 4 psi x 10 square inches = 40 pounds. 
Therefore, the total force exerted on the fluid is 40 pounds. 
The total area the force acts on is the sum of the areas of both pistons: 1 square inch + 10 square inches = 11 square inches. 
So the pressure on the narrow hose is (total force)/(total area) = 40 pounds/11 square inches = 3.64 psi, which we round to 4 psi.

Two Pistons Push Down on the Fluid Filling Two Cylinders