A workshop press employs a small piston of area connected to a large piston of area…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

A workshop press employs a small piston of area

5.0\,\text{cm}^2

connected to a large piston of area

0.40\,\text{m}^2

by a pipe filled with oil of density

900\,\text{kg\,m}^{-3}

. The operator can exert a maximum force of

400\,\text{N}

on the small piston. The press is required to lift loads up to

10\,000\,\text{N}

placed on the large piston. Using the data given, answer the following. (i) Derive an expression for the greatest vertical separation

h_{\max}

that may exist between the two pistons if the press is to meet the stated load requirement. (ii) Calculate

h_{\max}

for the numerical values provided. (iii) If the actual separation is half of

h_{\max}

, determine the load that can be lifted with the same

400\,\text{N}

effort.