Question

A dentist's chair with a patient in it weighs 2340 N. The output plunger of a...

A dentist's chair with a patient in it weighs 2340 N. The output plunger of a hydraulic system begins to lift the chair, when the dentist's foot applies a force of 78.1 N to the input piston. Neglect any height difference between the plunger and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

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Answer #1

Weight of the dentist's chair with the patient = F1 = 2340 N

Force applied by the dentist's foot = F2 = 78.1 N

Radius of the output plunger = R1

Cross-sectional area of the output plunger = A1 = R12

Radius of the input piston = R2

Cross-sectional area of the input piston = A2 = R22

Pressure in the output plunger = P1 = F1/A1

Pressure in the input piston = P2 = F2/A2

Pressure in the output plunger and the input piston is equal.

P1 = P2

Ratio of the radius of the plunger to the radius of the piston = 5.47

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