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 A ₂ is 10 square inches. A force of 4 pounds is exerted downward on piston 1, as shown.
The force F ₂ needed to keep piston 2 in place is 40 pounds.

Question

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 A ₂ is 10 square inches. A force of 4 pounds is exerted downward on piston 1, as shown.

Two pistons push down on the fluid filling two cylinders connected by a narrow hose, as shown in the figure. The area A <sub>1</sub> is 1 square inch, and the area A <sub>2</sub> is 10 square inches. A force of 4 pounds is exerted downward on piston 1, as shown. The force F <sub>2</sub> needed to keep piston 2 in place is 40 pounds.

The force F ₂ needed to keep piston 2 in place is 40 pounds.

Quizplus · Accepted Answer

The pressure in the fluid is equal throughout the connected system. So, the pressure exerted on piston 1 is the same as the pressure exerted on piston 2. Since piston 2 has 10 times the surface area of piston 1, the force exerted on piston 2 is 10 times the force exerted on piston 1. Therefore, the force needed to keep piston 2 in place is 10 times the force applied to piston 1, which is 40 pounds (4 x 10 = 40).

Two Pistons Push Down on the Fluid Filling Two Cylinders