Calculating Mass and Height Changes in a Hydraulic Lift

[mattmannmf]

A hydraulic lift has two connected pistons with cross-sectional areas 5 cm2 and 650 cm2. It is filled with oil of density 720 kg/m3.

a) What mass must be placed on the small piston to support a car of mass 1400 kg at equal fluid levels?

10.77 OK

b) With the lift in balance with equal fluid levels, a person of mass 80 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?

Now what i started off with was that pressure= mg/A (1480*9.8/ 650) and that equals density(g)(h)...so i got height change to be .003...but that's wrong

 

[mattmannmf]

so i figured out B..its 1.7

I just have no idea where to start for C

 

[nlightner]

Thank you for sharing your thought process. It seems like you have a good understanding of the concepts involved in this problem. However, there are a few errors in your calculations.

For part a), the correct formula to use is P1A1=P2A2, where P is the pressure, A is the cross-sectional area, and the subscripts 1 and 2 represent the two connected pistons. This formula is based on the principle of Pascal's law, which states that pressure applied to an enclosed fluid is transmitted uniformly throughout the fluid.

Using this formula, we can solve for the mass on the small piston:

P1A1=P2A2
(mass of car + mass on small piston) * g / A1 = mass of car * g / A2
mass on small piston = (mass of car * A1 / A2) - mass of car
= (1400 kg * 5 cm2 / 650 cm2) - 1400 kg
= 10.77 kg

For part b), we can use the same formula to find the equilibrium height difference:

P1A1=P2A2
(mass of car + mass on small piston + mass of person) * g / A1 = mass of car * g / A2
(height difference) = (mass of car * A1 / A2 + mass of person * A1 / A2) / (density * g)
= ((1400 kg * 5 cm2 / 650 cm2) + (80 kg * 5 cm2 / 650 cm2)) / (720 kg/m3 * 9.8 m/s2)
= 0.003 meters

For part c), the height of the car will drop by the same amount as the equilibrium height difference, which is 0.003 meters.

I hope this helps clarify the correct approach to solving this problem. Keep up the good work in your scientific studies!