How Does a Hydraulic Lift Maintain Equilibrium?

AI Thread Summary
A hydraulic lift operates on the principle of fluid mechanics, where two connected pistons maintain equilibrium through equal fluid levels. 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 1.77 m. The relationship between weight and height change is based on the conservation of volume and the proportionality of piston areas. Understanding these principles clarifies how the weight of the car and additional mass affect the lift's balance.
jrouse33
Messages
1
Reaction score
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!
 
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:
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Calculations for Hydraulic Jacks lifting a load
Replies
2
Views
3K
Calculating Mass and Height Changes in a Hydraulic Lift
Replies
1
Views
2K
How Does a Hydraulic Lift Work with Different Piston Sizes and Weights?
Replies
1
Views
2K
Solving a Hydraulic Lift: Mass, Volume and Height Differences
Replies
1
Views
3K
Applying Pascal's Law to a Hydraulic Lift Problem
Replies
4
Views
8K
Pascal's principle hydraulic lift with torque involved
Replies
4
Views
5K
Lifting a car using a hydraulic lift
Replies
3
Views
3K
Calculating Pressure for a Hydraulic Car Lift
Replies
5
Views
2K
Balancing a Hydraulic Lift with Two Pistons
Replies
1
Views
2K
How Does a Hydraulic Lift Work with Different Piston Sizes?
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top