Hydraulic lift with unequal piston areas and fluid levels

[Juntao]

A hydraulic lift has two connected pistons with cross-sectional areas 25 cm2 and 420 cm2. It is filled with oil of density 730 kg/m3.

a) What mass must be placed on the small piston to support a car of mass 1000 kg at equal fluid levels?
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?
c) How much did the height of the car drop when the person got in the car?
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a) Simple. Did F1/A1=F2/A2. Solved for mass.
m1*g/.0025m^2=m2*g/.0420m^2

m2 = 1000kg
solve for m1 i get 59.523kg

b) Ok. With the use of bernoulii's equation, the velocity is zero, so I get p1+rho*g*h1=p2+rho*g*h2
so (h1-h2)=(p2-p1)/(rho*g)

where p = pressure
A2=.0420m^2
A1=.0025m^2
p2= (mass car+guy)*g/A2
p1= 59.523kg*g/A1

sovle for h1-h2
I get 2.2835m, which is right.

c) Okay, I was thinking find the differnce in height when its only the car, then find the difference in heigh when guy is in car. Take the two answers, and subtract them from each other to get the answer, but its not working right.

 

[Doc Al]

Originally posted by Juntao
c) Okay, I was thinking find the differnce in height when its only the car, then find the difference in heigh when guy is in car. Take the two answers, and subtract them from each other to get the answer, but its not working right.

One side goes down (H₁), one side goes up (H₂). You know the difference in height, H = H₁ + H₂.

Now make use of the fact that the volume of the fluid (oil) must not change. This will give you enough info to solve for the individual height changes.

 

[M98Ranger]

To find the difference in height when it's only the car, we can use the equation from part a) and solve for h1-h2. Plugging in the values, we get h1-h2= 2.381m.

Then, to find the difference in height when the person is in the car, we can use the equation from part b) and solve for h1-h2 again. Plugging in the new values (mass of car + person), we get h1-h2= 2.2835m.

To find the actual difference in height, we can subtract the two values: 2.381m - 2.2835m = 0.0975m. This means that the height of the car dropped by 0.0975m when the person got in.