N"Solving Pressure of Hydraulically-Operated Chair

[naspri4]

Homework Statement

Imagine a hydraulically operated dentist's chair having a mass of 190.0 kg and in it is sitting a 52.8 kg patient. The large piston beneath the chair has a diameter of 5.00 cm, whereas the small piston, moved by a pedal on which the dentist steps, has a diameter of 1.00 cm. What is the pressure in the interconnecting fluid when the dentist operates the chair?
the answer is in Mpa

Homework Equations

F=PA

The Attempt at a Solution

so there was another question right below this that asked for how much force he must exert on the smaller piston, so using F=PA i found P to equal 121.24 then i used that number with the area of the smaller piston and found the F of the smaller pistion to be 95.17N. So i assume the pressure must be right, but i don't get what the first question is asking for because although it is labeled in Mpa the answer is still wrong.

(finding pressure)
190 + 52.8 = 242.8

242.8 * 9.8 = 2389.44

2389.44= (P)(A=(pie)(2.5squared))

2389.44=(P)(19.625)

P=121.24

(finding second answer)
F=(121.24)(A=(pie)(.5squared))

F=(121.24)(.785)

F=95.17

 

[Jhero]

N



Thank you for your question. After analyzing your attempt at a solution, I believe the issue lies in your calculation for the pressure in the interconnecting fluid. The equation you used, F=PA, is correct, but the value for the force (F) should be the weight of the entire system, which includes the dentist's chair and the patient. Therefore, the calculation should be as follows:

F = (190.0 kg + 52.8 kg) * 9.8 m/s^2 = 2389.44 N

Next, we can use the equation F=PA to find the pressure (P) in the interconnecting fluid:

2389.44 N = P * (π * 2.5 cm^2)

P = 121.24 kPa

To convert kPa to MPa, we divide by 1000:

P = 121.24 kPa / 1000 = 0.12124 MPa

Therefore, the pressure in the interconnecting fluid when the dentist operates the chair is 0.12124 MPa, or 121.24 kPa.

I hope this helps clarify the solution for the first question. Please let me know if you have any further questions.