A dentist’s chair with a patient in it weight 2100N. The output plunger of a hydraulic system begins to lift the chair, when the dentist’s foot applies of 55N to the input piston. Neglect any height difference between the plunder and the piston. What is the ratio of the radius of the plunger to the radius of the piston?

ratio of radii = √(ratio of areas)

ratio of forces is inverse of ratio of areas

To find the ratio of the radius of the plunger to the radius of the piston, we can use Pascal's principle, which states that when a fluid is confined in a container, any change in pressure is transmitted equally to all portions of the fluid and to the walls of its container.

In this scenario, the force applied to the input piston (dentist's foot) is 55N, and the weight of the chair is 2100N. The force on the output plunger can be calculated as follows:

Force on Input Piston = Force on Output Plunger

Using this relationship, we can set up the equation as:

Input Force/Input Area = Output Force/Output Area

Given that the input force is 55N and the weight of the chair is 2100N, and assuming the input and output pistons are circular, we can rewrite the equation as:

55N/(π * r₁²) = 2100N/(π * r₂²)

Where r₁ is the radius of the input piston and r₂ is the radius of the output plunger.

Now, let's simplify the equation:

55 / πr₁² = 2100 / πr₂²

Cross-multiplying, we have:

55 * πr₂² = 2100 * πr₁²

Dividing both sides by π:

55 * r₂² = 2100 * r₁²

Finally, we can find the ratio of the radius of the plunger to the radius of the piston by taking the square root:

√(r₂² / r₁²) = r₂ / r₁

So, the ratio of the radius of the plunger to the radius of the piston is equal to √(r₂² / r₁²), where r₂ is the radius of the output plunger and r₁ is the radius of the input piston.