Physics

Physics

Problem

A hydraulic press has an output ram with a circular face of diameter 0.25 m0.25\,\text{m}. The fluid inside must not exceed a pressure of 3.2×105 Pa3.2\times10^{5}\,\text{Pa}. A 450 kg steel slab already rests on the ram and must be supported along with any additional load. Calculate the greatest additional force (in newtons) that can be exerted on a sample without surpassing the pressure limit.
Intuitive explanation

Hydraulic presses work by transmitting pressure uniformly through an incompressible fluid—the same pressure acts everywhere inside. The key insight is that the maximum force the ram can support is limited by the pressure ceiling and the ram's area: rearrange P=F/AP = F/A to find Fmax=Pmax×AF_{\text{max}} = P_{\text{max}} \times A. Then subtract the force already needed to support the steel slab's weight to find how much additional load is allowed.

Intuitive explanation

Hydraulic presses work by transmitting pressure uniformly through an incompressible fluid—the same pressure acts everywhere inside. The key insight is that the maximum force the ram can support is limited by the pressure ceiling and the ram's area: rearrange P=F/AP = F/A to find Fmax=Pmax×AF_{\text{max}} = P_{\text{max}} \times A. Then subtract the force already needed to support the steel slab's weight to find how much additional load is allowed.

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