A green sedan weighing 25,000 Newtons is put on a lift supported by a piston with
a cross sectional area of 0.1 square meters. What is the minimum force that must
be exerted by the air compressor that pushes down on the oil in the reservoir of the lift system in order to lift the sedan if the cross-sectional area of the reservoir
is 1.0 square meter? (Hint:use Pascal’s Law.)
To solve this problem, we can use Pascal's Law, which states that pressure exerted on a fluid is transmitted equally in all directions. The formula we can use is:
Pressure_1/Area_1 = Pressure_2/Area_2
In this case, the pressure is caused by the force exerted by the air compressor pushing down on the oil in the reservoir. The given information is:
Force_1 (weight of the sedan) = 25,000 Newtons
Area_1 (cross-sectional area of the piston) = 0.1 square meters
Area_2 (cross-sectional area of the reservoir) = 1.0 square meter
Now we can calculate the pressure using the formula:
Pressure_1/Area_1 = Pressure_2/Area_2
Pressure_1 = Force_1 / Area_1
Pressure_2 = Pressure_1 * (Area_2 / Area_1)
Let's calculate the pressure:
Pressure_1 = 25,000 N / 0.1 m^2
= 250,000 N/m^2
Pressure_2 = 250,000 N/m^2 * (1.0 m^2 / 0.1 m^2)
= 2,500,000 N/m^2
Therefore, the minimum force that must be exerted by the air compressor is 2,500,000 Newtons.