How Does a Hydraulic Lift Work with Different Piston Sizes?

[Pat2666]

Okay, so I'm stuck on the last part of the problem :

A hydraulic lift has two connected pistons with cross-sectional areas 15 cm2 and 430 cm2. It is filled with oil of density 620 kg/m3.

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a) What mass must be placed on the small piston to support a car of mass 1600 kg at equal fluid levels?

kg *
55.8 OK

b) With the lift in balance with equal fluid levels, a person of mass 80 kg gets into the car. What is the equilibrium height difference in the fluid levels in the pistons?

m *
3.02 OK

c) How much did the height of the car drop when the person got in the car?

m

HELP: The fluid is incompressible, so volume is conserved.
HELP: Remember, one side will go up and one side will go down. The difference you calculated in part (b) was the sum of those two changes.

Okay, so I managed to find out the first two parts of the problem but I'm having trouble with Part C. Any way I attempt either comes out to the answer for B, or is just wrong. Since it mentioned that the volume is the same I thought that maybe the volumes of the cylindrical area displaced for each piston would be equal to one another (as you will see below). However, I came up with 0.109m as the height that the car moved, but it was wrong. I don't know what I'm doing wrong or what I might be missing completely. Any help would be greatly apprciated :)

My work :

http://img255.imageshack.us/img255/7595/workns5.jpg

 

[RTW69]

Your result looks fine to me. Another approach is Work-in=Work-out.

F1d1=F2d2

(3.02)(55.8)(9.80)= X(1680)(9.8)

X= .1003 m

 

[Moetasim]

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I can provide some insight into the problem and help you find the solution for Part C. First, it is important to understand the concept of Pascal's Law, which states that pressure applied to a confined fluid is transmitted equally in all directions. In the case of a hydraulic lift, this means that the pressure applied to the smaller piston will be transmitted to the larger piston.

In order to solve Part C, we need to consider the volume of the fluid displaced by the smaller piston when the person gets into the car. This volume will be equal to the volume of the fluid displaced by the larger piston, which will cause the car to drop.

Using the formula for volume of a cylinder (V=πr^2h), we can calculate the volume of the fluid displaced by the smaller piston:

V = π(0.075m)^2(0.109m) = 0.00265m^3

Since the volume of the fluid is conserved, this volume will also be displaced by the larger piston, causing the car to drop. We can use the same formula to solve for the height (h) of the car drop:

0.00265m^3 = π(0.215m)^2h

h = 0.00383m

Therefore, the height of the car dropped when the person got in is 0.00383m, or 3.83mm.

I hope this helps you understand the problem better and find the correct solution for Part C. Keep in mind the concept of Pascal's Law and the conservation of volume in order to solve these types of problems. Good luck!