Question

A dentist's chair with a person in it weighs 1675 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant's foot exerts a force of 39 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston

Answer 1

The ratio of the area of the plunger to the area of the piston in the hydraulic system is approximately 42.95.

Step-by-step explanation:

The ratio of the area of the plunger to the area of the piston can be determined using the equation of force ratios in a hydraulic system:

Force out/Force in = Area in/Area out

In this case, the force out is the weight of the chair (1675 N) and the force in is the force exerted by the dental assistant's foot (39 N). Let's assume that the area of the plunger is Aout and the area of the piston is Ain. So, the equation can be written as:

1675 N / 39 N = Ain / Aout

Cross-multiplying and solving for the ratio of the areas:

Aout / Ain = 1675 N / 39 N = 42.95

Therefore, the ratio of the area of the plunger to the area of the piston is approximately 42.95.