A hydraulic lift has 2000 N applied to an input piston that has an area of 50cm2. The Output piston has an area of 200cm2.
A) what is the pressure on the liquid exerted by the input piston?
B) will the force on the output piston be the same or not? Explain why?
Answer
A) To find the pressure on the liquid exerted by the input piston, we can use the formula:
Pressure = Force / Area
Given:
Force = 2000 N
Area = 50 cm^2
Converting the area to square meters:
Area = 50 cm^2 * (1 m / 100 cm)^2 = 0.005 m^2
Now we can substitute the values into the formula:
Pressure = 2000 N / 0.005 m^2 = 400,000 Pa
So, the pressure on the liquid exerted by the input piston is 400,000 Pa.
B) No, the force on the output piston will not be the same. The force exerted on the output piston depends on the pressure exerted by the input piston and the area of the output piston, according to the formula:
Force = Pressure * Area
Given:
Pressure = 400,000 Pa
Area = 200 cm^2
Converting the area to square meters:
Area = 200 cm^2 * (1 m / 100 cm)^2 = 0.02 m^2
Substituting the values into the formula:
Force = 400,000 Pa * 0.02 m^2 = 8000 N
Therefore, the force on the output piston will be 8000 N, which is different from the force applied to the input piston. This difference in force is due to the difference in the areas of the two pistons. The output piston has a larger area, so it will be able to exert a greater force even though the pressure remains the same.
To answer these questions, we need to use the principles of Pascal's Law, which states that when pressure is applied to a fluid in an enclosed space, it is transmitted equally in all directions.
A) To find the pressure on the liquid exerted by the input piston, we can use the formula:
Pressure = Force / Area
We are given that 2000 N is applied to the input piston, and it has an area of 50 cm^2. To get the pressure, we convert the area from cm^2 to m^2 by dividing it by 10,000:
Area (m^2) = Area (cm^2) / 10,000
Area (m^2) = 50 cm^2 / 10,000
Area (m^2) = 0.005 m^2
Now we can calculate the pressure:
Pressure = 2000 N / 0.005 m^2
Pressure = 400,000 Pa
Therefore, the pressure on the liquid exerted by the input piston is 400,000 Pascal (Pa).
B) According to Pascal's Law, the pressure in a fluid is transmitted equally in all directions. Since the hydraulic lift is an enclosed system, the pressure exerted by the input piston will be transmitted to the output piston.
However, the force on the output piston will not be the same. The force exerted on a piston is calculated using the formula:
Force = Pressure x Area
We have already calculated that the pressure on the liquid exerted by the input piston is 400,000 Pa. The output piston has an area of 200 cm^2, which we convert to m^2 by dividing by 10,000:
Area (m^2) = 200 cm^2 / 10,000
Area (m^2) = 0.02 m^2
Now we can calculate the force on the output piston:
Force = 400,000 Pa x 0.02 m^2
Force = 8,000 N
Therefore, the force on the output piston is 8,000 N, which is different from the 2,000 N applied to the input piston. The force is greater on the output piston due to the larger area.