Calculating Force to Raise a Dentist Chair

[BuBbLeS01]

Homework Statement

A dentist's chair of mass 207kg is supported by a hydraulic lift having a large piston of cross-sectional area 1403.0cm^2. The dentist has a foot pedal attached to a small piston of cross-sectional area 78.0cm^2. What force must be applied to the small piston to raise the chair.

Homework Equations

P=F/A
Fp/Ap = Fc/Ac

The Attempt at a Solution

Fp = Fc/Ac * Ap
Fp = 207kg/1403 * 78 = 112.78

Okay so I have already gotten the answer 112.78N but I don't understand a few things about this question...
- Why does Fp/Ap = Fc/Ac??
- Why is 207kg relate to 1403cm^2?
- What is the subscripts p and c?

 

[rock.freak667]

Suggestion in your calculations when you said...

Fp = 207kg/1403 * 78 = 112.78

F=mg...so the force should be the weight..so you have to multiply by 9.81Nkg^-1 or whatever value you take as g and convert the cm^2 to m^2


"Why does Fp/Ap = Fc/Ac??"

Does this not mean that $P_p=P_c$ which just basically says that pressure is transmitted equally throughout a fluid...i.e. the pressure at one end is equal to the pressure at the other.

the subscripts p and c would be piston and chair respectively

 

[ogb p]

I would like to clarify some of the concepts in this problem.

Firstly, the equation P=F/A is the formula for pressure, where P is pressure, F is force, and A is area. This equation tells us that the pressure exerted by a force is directly proportional to the force and inversely proportional to the area over which the force is applied.

In this problem, the hydraulic lift works based on the principle of Pascal's Law, which states that pressure applied to a fluid in a closed container is transmitted equally in all directions. This means that the pressure applied by the small piston (Fp/Ap) will be transmitted to the large piston (Fc/Ac) and will result in the same pressure on the larger piston. This is why Fp/Ap is equal to Fc/Ac.

The 207kg represents the mass of the dentist's chair, and it is related to the 1403cm^2 because the chair is supported by the hydraulic lift. The weight of the chair is distributed over the large piston, which has an area of 1403cm^2. This is why the mass is related to the area.

The subscripts p and c represent the small and large pistons, respectively. They are used to differentiate between the two pistons and their corresponding forces and areas.

In conclusion, the force required to raise the dentist's chair can be calculated by using the equation Fp/Ap = Fc/Ac, where Fp is the force applied to the small piston, Ap is the area of the small piston, Fc is the force on the large piston, and Ac is the area of the large piston. By plugging in the values given in the problem, we can calculate the required force to be 112.78N.