A hydraulic lift is designed to lift cars with maximum mass of 3000kg. The area of cross section of piston carrying the load is 425 cm2. The maximum pressure on smaller piston is
Question
A hydraulic lift is designed to lift cars with maximum mass of 3000kg. The area of cross section of piston carrying the load is 425 cm2. The maximum pressure on smaller piston is
Solution
The maximum pressure on the smaller piston can be calculated using Pascal's law, which states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
The formula for pressure is:
P = F/A
where: P is the pressure, F is the force, A is the area.
In a hydraulic lift, the force is the weight of the car, which is the mass of the car times the acceleration due to gravity.
So, F = m*g
where: m is the mass of the car, which is 3000 kg, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
So, F = 3000 kg * 9.8 m/s^2 = 29400 N.
The area A is given as 425 cm^2. To convert this to m^2 (since the other units are in kg and m/s^2), we use the conversion 1 m^2 = 10000 cm^2.
So, A = 425 cm^2 * (1 m^2 / 10000 cm^2) = 0.0425 m^2.
Now we can calculate the pressure P:
P = F/A = 29400 N / 0.0425 m^2 = 691764.7058823529 Pa.
So, the maximum pressure on the smaller piston is approximately 691765 Pa.
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