Lifting a car using a hydraulic lift

In summary, if the level increases in one arm, it should decrease in the other one. So the oil level in the compressed arm is below zero.
1. The hydraulic lift at a repair shop is filled with oil. The car rests on a 25-cm-diameter piston. To lift the car, compressed air is pushed down on the 6-cm-diameter piston.
a) What air-pressure force will support a 1300kg car level with the compressed air piston?
b) How much must the air-pressure-force be increased to lift the car by 2m.

2. Homework Equations :
p = p + ρ*g*h
ρ=900kg/m^2

3. The Attempt at a Solution
I did a) by doing p + ρ*g*0 + F1/A1 = p + ρ*g*0 + F2/A2
Then used F1 = F2 * (A1/A2) to find that F1 is 730N, which is correct according to the solutions.

Then I attempted b) and used a similar approach.
I tried:
p + F1/A1 + ρ*g*(0) = p + ρ*g*h + F2/A2*
So I rearranged to get F1 = A1*ρ*h*g + (F2)*(A1/A2)
Finding A1, A2, and F2 easily, and using h =2m and ρ=900kg/m^3 and g = 9.8m/s^2, I keep getting F1 = 784N. So the increase in force should be 784N - 730N = 54N, but my book tells me the answer is 920N.

b) How much must the air-pressure-force be increased to lift the car by 2m.

Then I attempted b) and used a similar approach.
I tried:
p + F1/A1 + ρ*g*(0) = p + ρ*g*h + F2/A2*
So I rearranged to get F1 = A1*ρ*h*g + (F2)*(A1/A2)
Finding A1, A2, and F2 easily, and using h =2m and ρ=900kg/m^3 and g = 9.8m/s^2, I keep getting F1 = 784N. So the increase in force should be 784N - 730N = 54N, but my book tells me the answer is 920N.

The amount of oil does not change during lifting the car. If the level increases in one arm, it should decrease in the other one. So the oil level in the compressed arm is below zero.

ehild.

1 person
Thank you so much! I used the volume's of liquid displaced to calculate how much the smaller piston would go down and found that it would move down by 34.72m, while as the other larger piston would move up by 2m.
Then I used the following formula to find F1 = A1*(ρ*g*h) + F2*(A1/A2)
And got 1650N
Then 1650-730 =920N =D Thank you very much!

You are welcome

ehild

I don't understand why it is different.

Your approach for part b) is correct, but you made a mistake in your calculations. The correct equation is p + F1/A1 + ρ*g*0 = p + ρ*g*h + F2/A2.

Solving for F1, we get F1 = (A1*ρ*g*h + F2*A1/A2) / (1 - A1/A2). Plugging in the values, we get F1 = (0.0025m^2 * 900kg/m^3 * 9.8m/s^2 * 2m + 730N * 0.0025m^2/0.00036m^2) / (1 - 0.0025m^2/0.00036m^2) = 920N.

It seems like you forgot to divide by (1 - A1/A2) in your calculations, which resulted in the incorrect answer.

What is a hydraulic lift?

A hydraulic lift is a type of machine that uses fluid pressure to lift heavy objects. It works by applying force to a small area, which is then transmitted to a larger area, resulting in a greater amount of force being exerted.

How does a hydraulic lift work?

A hydraulic lift works through the use of two connected cylinders, one larger than the other. When force is applied to the smaller cylinder, it pushes against the fluid in the system, which then transfers the force to the larger cylinder. This results in a multiplication of force, allowing the lift to raise heavy objects with ease.

What are the components of a hydraulic lift?

A hydraulic lift typically consists of a pump, cylinders, a reservoir, valves, and hydraulic fluid. The pump is responsible for creating pressure in the system by moving the hydraulic fluid, which is stored in the reservoir. The valves control the flow of the fluid, and the cylinders are what actually lift the object.

What are the benefits of using a hydraulic lift?

One of the main benefits of using a hydraulic lift is its ability to lift heavy objects with relatively little force. It is also more precise and controllable compared to other lifting methods, making it ideal for delicate objects. Additionally, hydraulic lifts require minimal maintenance and can last for a long time.

Are there any potential risks or dangers to using a hydraulic lift?

Like any machinery, there are potential risks associated with using a hydraulic lift. The most common risks are hydraulic fluid leaks, which can cause slips and falls, and mechanical failures, which can result in objects falling. It is important to follow proper safety protocols and regularly maintain the lift to minimize these risks.

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