How Does a Hydraulic Lift Work with Different Piston Sizes and Weights?

AI Thread Summary
A hydraulic lift operates using two connected pistons with different cross-sectional areas, allowing it to support varying weights. To balance a car weighing 1100 kg, a mass of 35.86 kg must be placed on the smaller piston. When a 70 kg person enters the car, the equilibrium height difference in the fluid levels between the pistons is 2.72 m. The challenge arises in calculating how much the car drops versus how much the weight on the other piston rises, as the total height difference must be shared between both movements. Understanding these dynamics is crucial for accurately determining the lift's response to added weight.
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Homework Statement


A hydraulic lift has two connected pistons with cross-sectional areas 15 cm2 and 460 cm2. It is filled with oil of density 560 kg/m3.


Homework Equations


a)What mass must be placed on the small piston to support a car of mass 1100 kg at equal fluid levels?
A:35.86 kg
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?
A:2.72 m
c) How much did the height of the car drop when the person got in the car?


The Attempt at a Solution


Take the difference in height when its the only the car, then find difference in height of car + guy. Subtract those two. But its not working.
 
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It seems to me that, when the guy got in the car, the car went down but the 38.5 kg weight on the other piston went up. So you have to share out that 2.72 metres between how much the car went down and how much the other piston went up.
 

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