Hydraulic Lift equilibrium

In summary, a hydraulic lift with two connected pistons of different cross-sectional areas and filled with oil of density 570 kg/m3 is discussed. The questions involve calculating the mass needed on the smaller piston to support a car of mass 1300 kg, the equilibrium height difference when a person of mass 70 kg gets into the car, and the change in height of the car when the person enters. The solution involves using the conservation of volume and the proportional relationship between the piston areas and height changes.
  • #1
jrouse33
1
0

Homework Statement



A hydraulic lift has two connected pistons with cross-sectional areas 25 cm2 and 700 cm2. It is filled with oil of density 570 kg/m3.

a) What mass must be placed on the small piston to support a car of mass 1300 kg at equal fluid levels? (answer: 46.4kg)

b) With the lift in balance with equal fluid levels, a person of mass 70 kg gets into the car. What is the equilibrium height difference in the fluid levels in the pistons? (answer: 1.77m)

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

The Attempt at a Solution



I know that the fluid is incompressible therefore the volume is conserved. I also know that the height changed is proportional to the area of each of the pistons. I know that A1*d1=A2*d2 where d1 is the distance piston 1 is pushed down and the volume is A1 that flowed into the piston.

Where I am confused is how do we relate the weight to the change in height.

Any help would greatly be appreciated!
 
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  • #2
If I say : the difference in fluid heights provides a weight that balance with that of the car.
Does that help you in understanding their relations?:smile:
 
  • #3


I would like to clarify the concept of equilibrium in a hydraulic lift. In this scenario, the lift is in equilibrium when the forces acting on the two pistons are balanced, causing equal fluid levels in the two pistons. This means that the pressure exerted by the fluid on each piston is equal.

To answer the given questions, we can use the principle of Pascal's law, which states that the pressure applied to a confined fluid is transmitted equally in all directions. This means that the pressure exerted on the smaller piston (p1) is equal to the pressure exerted on the larger piston (p2).

a) To support a car of mass 1300 kg, the force exerted by the fluid on the larger piston (p2) must be equal to the weight of the car (1300 kg x 9.8 m/s2 = 12740 N). Using the equation p=F/A, where p is pressure, F is force, and A is area, we can calculate the pressure on the larger piston as p2 = 12740 N / 700 cm2 = 18.2 N/cm2. Since the pressure is equal on both pistons, the force exerted on the smaller piston (p1) must also be 18.2 N/cm2. Using the same equation, we can calculate the mass needed to exert this force as m = F/A = 18.2 N/cm2 x 25 cm2 = 455 grams or 0.455 kg. Therefore, the mass needed on the smaller piston to support the car is 0.455 kg.

b) When a person of mass 70 kg gets into the car, the weight of the car and the person increases to 1370 kg. Using the same method as above, we can calculate the new pressure on the larger piston as p2 = 1370 kg x 9.8 m/s2 / 700 cm2 = 19.7 N/cm2. Since the pressure on the smaller piston remains the same, the force exerted on it must also increase to balance the pressure. Therefore, the new force on the smaller piston is 19.7 N/cm2 x 25 cm2 = 492.5 N.

To find the equilibrium height difference, we can use the equation p=F/A, where p is pressure, F is force, and A is area. The height difference
 

1. What is a hydraulic lift?

A hydraulic lift is a machine that uses liquid, usually oil, to transmit pressure from one point to another in order to lift heavy objects. It consists of a pump, a cylinder and a piston, and a control valve.

2. How does a hydraulic lift work?

When force is applied to the pump, it pushes the liquid from the reservoir into the cylinder, which causes the piston to move. As the piston moves, it pushes against the object that needs to be lifted, and the pressure is transmitted through the liquid, causing the object to be lifted.

3. What is the principle of equilibrium in a hydraulic lift?

The principle of equilibrium in a hydraulic lift states that the pressure applied to the liquid in the system is transmitted equally throughout the system. This means that the force applied to the small piston (or input force) is multiplied and transmitted to the larger piston (or output force).

4. How does the area of the pistons affect the equilibrium in a hydraulic lift?

The area of the pistons affects the equilibrium in a hydraulic lift because the pressure exerted by the liquid is directly proportional to the area of the piston. This means that a larger piston will exert more force than a smaller piston, and the equilibrium will be maintained as long as the pressure remains constant.

5. What are some common uses of hydraulic lifts?

Hydraulic lifts have a wide range of uses, including lifting heavy objects in construction and manufacturing, elevators in buildings, and hydraulic car lifts in mechanic shops. They are also commonly used in hydraulic jacks and lifts for cars and other vehicles.

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