# Solving a Hydraulic Lift: Mass, Volume and Height Differences

• bricker9236
In summary, a hydraulic lift with two connected pistons of cross-sectional areas 25 cm2 and 250 cm2, filled with oil of density 510 kg/m3, can support a 1200 kg car at equal fluid levels if a mass of 120 kg is placed on the small piston. When a person of mass 90 kg enters the car, the equilibrium height difference in the fluid levels in the pistons is 7.0588 m, with one cylinder going down and the other going up. To find the height difference of the car when the person gets in, an equation can be written using the fact that the volume of oil pushed out of one cylinder is equal to the volume of oil pushed into the other cylinder
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?

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.

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.

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.

## 1. What is a hydraulic lift?

A hydraulic lift is a type of machine that uses fluid pressure to lift or lower heavy objects. It works on the principle of Pascal's law, which states that when pressure is applied to a confined fluid, the pressure is transmitted equally in all directions.

## 2. How can I calculate the mass of an object using a hydraulic lift?

To calculate the mass of an object using a hydraulic lift, you will need to know the volume of the object and the difference in height between the starting and ending positions. You can then use the formula: mass = density x volume x gravitational acceleration. The density of the object can usually be found in a reference book or online.

## 3. What factors affect the lifting capacity of a hydraulic lift?

The lifting capacity of a hydraulic lift is affected by several factors, including the size and strength of the pump, the diameter and length of the hydraulic cylinders, and the type of fluid used. The height difference between the starting and ending positions also plays a role in the lifting capacity.

## 4. How do I troubleshoot problems with a hydraulic lift?

If your hydraulic lift is not functioning properly, the first step is to check the fluid levels and make sure there are no leaks. You should also check the condition of the pump, cylinders, and valves for any signs of damage or wear. If you are unable to identify the issue, it is best to consult a professional for proper troubleshooting and repairs.

## 5. Can a hydraulic lift be used for lifting people?

No, hydraulic lifts are not designed or safe for lifting people. They are primarily used for lifting heavy objects in industrial or automotive settings. It is important to follow all safety guidelines and use proper lifting equipment when handling heavy objects to prevent accidents and injuries.

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