In a hydraulic lift an extendable chamber of diameter D is connected to a pipe of diameter d ≪ D, as shown in Fig. P4.2. Both are filled with an oil of density ρ. During lifting a pump delivers additional oil until the platform reaches its final height h₂. The pump is then shut off and a pressure P₁ is maintained at height h₁ in the pipe.

(a) Relate the pressure P₂ at the base of the stationary platform to P₁ and the dimensions.

(b) Derive an expression for the total mass m (load plus platform) that can be supported in the position shown.

(c) A friend who knows that force equals pressure times area is puzzled that a large load can be supported, even though with d ≪ D the pressure force at position 1 is much smaller than that at position 2. What is his or her misconception?

Transcribed Image Text:

1₂ Load m D Air P= Po - P= P₂ = ? Figure P4.2 Hydraulic lift in a raised position. d P= P₁ E h₁