A dentist's chair with a patient in it weighs 2260 N. The output plunger of a hydraulic system begins to lift the chair when the dentist's foot applies a force of 61 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?

rplunger / rpiston =

F2/F1 = S2/S1 =πR^2/πr^2= (R/r)^2

R/r =sqrt(F2/F1)

To solve this problem, we can apply Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.

Let's denote the radius of the plunger as rplunger and the radius of the piston as rpiston.

According to Pascal's law, the pressure applied to the input piston is equal to the pressure exerted by the output plunger. The pressure is given by:

Pressure = Force / Area

The force applied to the input piston is 61 N, and since the plunger and the piston are cylindrical in shape, the area can be calculated as:

Area = π * r^2

Since the pressure is the same, we can set up the following equation:

(61 N) / (π * rpiston^2) = (2260 N) / (π * rplunger^2)

Now, let's simplify the equation by canceling out π:

61 / (rpiston^2) = 2260 / (rplunger^2)

To find the ratio of the radius of the plunger (rplunger) to the radius of the piston (rpiston), we can rearrange the equation as follows:

(rplunger^2) / (rpiston^2) = (2260 N) / (61 N)

Taking the square root of both sides:

(rplunger / rpiston) = sqrt((2260 N) / (61 N))

Now, let's calculate this value:

(rplunger / rpiston) = sqrt(37.049)

Therefore, the ratio of the radius of the plunger to the radius of the piston is approximately:

rplunger / rpiston ≈ 6.086