Answer to Question #243393 in Physics for dina

Question #243393

A cylinder hydraulic press has a small piston with a diameter of 3 m, and the diameter

of the large piston is unknown. Suppose a force of 800 N is applied onto the small

piston to lift the 250 kg load. The hydraulic press follows Pascal principle.

i)

Calculate the diameter of the large piston.

ii)

Estimate the force needed if additional load of 50 kg is added. 


1
Expert's answer
2021-09-28T11:11:50-0400

i) The diameter is


"D=\\sqrt{\\frac{4A}{\\pi}}."

The weight the force of the piston must overcome is


"W=Mg=250\u00b79.8=2450\\text{ N}."

Find the mechanical advantage:


"\\text{ma}=\\frac{W}{F}=\\frac{A}{a},\\\\\\space\\\\\nA=a\\frac WF."

Here a - the area of the smaller piston. Hence:


"D=\\sqrt{\\frac{4aW}{F\\pi}}=d\\sqrt{\\frac{W}{F}}=3\\sqrt{\\frac{2450}{800}}=5.25\\text{ m}."

ii) The force is


"F_n=W_n\\frac{a}{A}=(250+50)9.8\u00b7\\frac{3^2}{5.25^2}=960\\text{ N}."



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