How Does a Hydraulic Lift Maintain Equilibrium?

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SUMMARY

The discussion centers on the mechanics of a hydraulic lift with two pistons of areas 25 cm2 and 700 cm2, filled with oil of density 570 kg/m3. To support a car weighing 1300 kg, a mass of 46.4 kg must be placed on the smaller piston. When a 70 kg person enters the car, the equilibrium height difference between the fluid levels in the pistons is calculated to be 1.77 m. The participant seeks clarification on how to relate the weight of the car and the person to the change in height of the fluid levels.

PREREQUISITES
  • Understanding of Pascal's Principle in hydraulics
  • Knowledge of fluid mechanics, specifically incompressible fluids
  • Familiarity with the concept of pressure and its relation to force and area
  • Basic algebra for solving equations involving area and height
NEXT STEPS
  • Study Pascal's Principle and its applications in hydraulic systems
  • Learn about the relationship between pressure, force, and area in fluid mechanics
  • Explore the concept of volume conservation in incompressible fluids
  • Investigate the mathematical derivation of hydraulic lift equations
USEFUL FOR

Students studying physics, engineers working with hydraulic systems, and anyone interested in understanding the principles of fluid mechanics and hydraulic lifts.

jrouse33
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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!
 
Physics news on Phys.org
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:
 

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