Calculating Mass to Support Car Weight on Hydraulic Lift

In summary, a hydraulic lift with two connected pistons (with cross-sectional areas of 5 cm^2 and 550 cm^2) filled with oil of density 520 kg/m3 is being used to support a car of mass 1500 kg. The formula used to calculate the necessary mass to be placed on the small piston is F=mg(A1/A2), but this attempted solution was incorrect. The actual solution requires just the ratio of the two areas (5cm/550cm)^2 to be multiplied by the mass and gravitational constant. The question of whether the oil density is relevant in this problem is discussed in a separate forum post.
  • #1
mujadeo
103
0

Homework Statement



A hydraulic lift has two connected pistons with cross-sectional areas 5 cm^2 and 550 cm^2. It is filled with oil of density 520 kg/m3.


a) What mass must be placed on the small piston to support a car of mass 1500 kg at equal fluid levels?



Homework Equations


Is the oil density a red herring in this question?


The Attempt at a Solution



F = mg (A1/A2)

F = mg (5cm/550cm)^2

F = (1500kg)(9.81)(5cm/550cm)^2

F = 1.261N = wrong!

please help!
 
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  • #2
A hydraulic system is just ratios.
In this case just the ratio of the two areas
 
  • #3
> F = (1500kg)(9.81)(5cm/550cm)^2


??
Re-think...
 

1. How do you calculate the mass needed to support a car's weight on a hydraulic lift?

The mass needed to support a car's weight on a hydraulic lift can be calculated by dividing the weight of the car by the gravitational acceleration (9.8 m/s^2). This will give you the mass in kilograms.

2. What is the formula for calculating the weight of a car?

The weight of a car can be calculated by multiplying its mass in kilograms by the gravitational acceleration (9.8 m/s^2). This will give you the weight in Newtons.

3. How do you determine the maximum weight a hydraulic lift can support?

The maximum weight a hydraulic lift can support is determined by its lifting capacity, which is usually specified by the manufacturer. This information can be found in the lift's manual or specifications.

4. What is the importance of calculating the mass for a hydraulic lift?

Calculating the mass is important for a hydraulic lift as it helps determine the maximum weight it can safely support. It also ensures that the lift is not overloaded, which can lead to accidents and damage to the lift.

5. Can the mass of a car change depending on the type of hydraulic lift being used?

No, the mass of a car does not change depending on the type of hydraulic lift being used. However, the lifting capacity of the lift may vary, so it is important to check the manufacturer's specifications to ensure the lift can safely support the weight of the car.

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