In a hydraulic lift, the maximum gauge pressure is 16.70 atm. If the diameter of the output line is 24.6 cm, what is the heaviest vehicle that can be lifted?
The answer is 80400 N. How do I get this answer? Isn't weight measured in kg? Thank you in advance.
I have tried to follow the similar problem under the "related questions", but I get 5.29e+6 N from doing it this way.
Kg is unit for mass and Newton is the unit for weight.( weight is a force W=mg)
Max. wt.that can be lifted = Pressure * area
= 1.01*10^5*16.7*3.14*0.123^2 N
=80126 N
Thank you!
By the way, using 101325 instead of 1.01e+05 and using pi instead of 3.14 gives a more accurate answer.
Using these values gives me 80425.39066 N, which rounds down to 80400 N.
To calculate the weight of the heaviest vehicle that can be lifted using the hydraulic lift, we need to understand that pressure is force per unit area.
First, convert the maximum gauge pressure from atm to Pascals (Pa). 1 atm is equal to 101,325 Pa.
16.70 atm * 101,325 Pa/atm = 1,679,192.5 Pa
Next, we need to determine the force exerted by the lift. The formula to calculate force using pressure and area is:
Force = Pressure * Area
Given the diameter of the output line (24.6 cm), we can calculate the radius (R) by dividing the diameter by 2:
Radius (R) = Diameter / 2 = 24.6 cm / 2 = 12.3 cm
Convert the radius to meters (m) by dividing it by 100:
Radius (R) = 12.3 cm / 100 = 0.123 m
To find the area (A) of the output line, we use the formula for the area of a circle:
Area (A) = π * R²
where π (pi) is approximately 3.14159.
Area (A) = 3.14159 * (0.123 m)²
Calculate the area:
Area (A) = 0.047663 m²
Now we can calculate the force using the formula mentioned earlier:
Force = Pressure * Area
Force = 1,679,192.5 Pa * 0.047663 m²
Force = 80,040.27495 N
Therefore, the heaviest vehicle that can be lifted is approximately 80,400 N.
Regarding your questions about measurements, weight is typically measured in Newtons (N), which is a unit of force. The kilogram (kg) is a unit of mass, not weight. However, weight can be calculated using the formula:
Weight = Mass * Gravity
where gravity is approximately 9.8 m/s². So, if you have the mass in kilograms, you can calculate the weight in Newtons using this formula.