Solving a Hydraulic Lift: Mass, Volume and Height Differences

[bricker9236]

Homework Statement

A hydraulic lift has two connected pistons with cross-sectional areas 25 cm2 and 250 cm2. It is filled with oil of density 510 kg/m3.


a) What mass must be placed on the small piston to support a car of mass 1200 kg at equal fluid levels? I got this answer - 120 kg

b) With the lift in balance with equal fluid levels, a person of mass 90 kg gets into the car. What is the equilibrium height difference in the fluid levels in the pistons?
i got this answer 7.0588m

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

C is the part that i am very confused on. I thought i was doing it correct and apparently not.

Homework Equations

h1+h2 = 7.0588
I thought this was the equation i used to figure out part C but i am just lost on it.

The Attempt at a Solution

above.

 

[Delphi51]

One cylinder goes down h1, the other up h2. Their total is 7.0588 m.
The volume of oil pushed out of the first cylinder equals the volume of oil pushed into the other cylinder. If you write an equation for this fact, you'll have a second equation relating h1 and h2. Then you can solve the two equations as a system to find h1 and h2.

 

[kerimek]

To solve part C, we need to use the equation of continuity, which states that the volume flow rate through a pipe is constant. In this case, the volume flow rate is the same for both sides of the hydraulic lift. We can express this as:

A1v1 = A2v2

Where A1 and A2 are the cross-sectional areas of the pistons, and v1 and v2 are the velocities of the fluid on each side.

Since the lift is in equilibrium, the velocities on both sides are the same, so we can rewrite the equation as:

A1h1 = A2h2

Where h1 and h2 are the heights of the fluid on each side.

To solve for the change in height of the car, we need to find the difference between the initial height (h1) and the final height (h2) when the person gets in the car. We can express this as:

Δh = h2 - h1

Since we know the initial and final heights from parts A and B, we can plug those values into the equation and solve for the change in height:

Δh = (7.0588 m) - (5.8824 m) = 1.1764 m

Therefore, the height of the car drops by 1.1764 meters when the person gets in the car. This is because the volume of the car (which is equal to the volume of the fluid displaced by the car) is now distributed between the two pistons, causing a difference in height between them.