FYKOS Year 39 Series 5 Problem 3 — hydraulic W · FYKOS 39 #39.5.3

Physics · mechanics

Problem

Consider a hydraulic press using three pistons with cross-sectional areas S1S_1, S2S_2, S3S_3 and masses m1m_1, m2m_2, m3m_3. Initially, they are at the same height. What is the acceleration of piston 1 at the moment when we release all of them simultaneously? Mechanics of a point mass Hydromechanics
Intuitive explanation

The key is recognizing that all pistons are connected by the same incompressible fluid, so their accelerations are linked through a constraint: volume conservation means S1a1+S2a2+S3a3=0S_1 a_1 + S_2 a_2 + S_3 a_3 = 0. Write Newton's second law for each piston (accounting for weight and pressure forces), then solve the system of equations to find a1a_1—the larger pistons effectively act as mechanical advantages that resist the motion of smaller ones.

Intuitive explanation

The key is recognizing that all pistons are connected by the same incompressible fluid, so their accelerations are linked through a constraint: volume conservation means S1a1+S2a2+S3a3=0S_1 a_1 + S_2 a_2 + S_3 a_3 = 0. Write Newton's second law for each piston (accounting for weight and pressure forces), then solve the system of equations to find a1a_1—the larger pistons effectively act as mechanical advantages that resist the motion of smaller ones.

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