The maximum gauge pressure in a hydraulic lift is 19.0 atm. What is the largest size vehicle (kg) it can lift if the diameter of the output line is 32.0 cm?
figure not the gauge pressure, but the pressure absolute in the tire, that is what is pressing on the lift.
absolute pressure*areaofcontact= lift
figure area of contact: PI *radius^2
To find the largest size vehicle that the hydraulic lift can lift, we need to consider the maximum gauge pressure and the diameter of the output line.
Step 1: Convert the maximum gauge pressure from atm to pascal (Pa).
1 atm is equal to 101,325 Pa. Therefore, the maximum gauge pressure of 19.0 atm is equal to 19.0 * 101325 = 1,924,175 Pa.
Step 2: Calculate the area of the output line.
The area of a circle is calculated using the formula A = π * r^2, where A is the area and r is the radius. Since we are given the diameter, we need to divide it by 2 to get the radius.
Given the diameter of the output line as 32.0 cm, the radius (r) is 32.0 cm / 2 = 16.0 cm = 0.16 m.
Using the formula for the area of a circle, A = π * r^2, we have:
A = π * (0.16)^2 = 0.08025 m^2.
Step 3: Calculate the force that the hydraulic lift can provide.
Force (F) is equal to pressure (P) multiplied by area (A). Therefore, using the maximum gauge pressure found in step 1 and the area of the output line found in step 2, we can calculate the force.
F = P * A = 1,924,175 Pa * 0.08025 m^2 = 154,810 N.
Step 4: Convert the force from newtons to kilograms.
To convert the force to kilograms, we need to divide it by the acceleration due to gravity, which is approximately 9.8 m/s^2.
Weight (W) = Force (F) / Acceleration due to gravity (g).
W = 154,810 N / 9.8 m/s^2 = 15,811.2 kg.
Therefore, the largest size vehicle that the hydraulic lift can lift is approximately 15,811.2 kg.
First conver atm to N/m^2. 1 atm = 1.013 x10^5 N/m^2.
Force F=mg
The pressure is the force, gravity is 9.8 m/s^2, the diameter is in centimeters, so convert to meters and take half, you don't know m (mass).
The formula you use is P = F/A.
So you will have a formula that looks like
P = m (9.8 m/s^2) / radius
Plug in your numbers and the result will be in kg, which is the weight that can be lifted.