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 find the minimum force needed to lift the sedan, we can use Pascal's Law. Pascal's Law states that when pressure is applied to a non-compressible fluid in a closed system, the pressure is transmitted equally in all directions.
In this case, the lift system consists of a piston with a cross-sectional area of 0.1 square meters and a reservoir with a cross-sectional area of 1.0 square meter.
First, let's calculate the pressure exerted by the sedan on the lift system:
Pressure = Force / Area
Here, the force exerted by the sedan is given as 25,000 Newtons and the area of the piston is 0.1 square meters.
Pressure = 25,000 N / 0.1 m^2
Pressure = 250,000 N/m^2 (or Pascal, since 1 Pascal = 1 N/m^2)
According to Pascal's Law, this pressure will be transmitted equally to the fluid in the reservoir.
Now, we need to find the force exerted by the air compressor on the oil in the reservoir to counteract the pressure exerted by the sedan.
Force = Pressure x Area
Here, the pressure is 250,000 N/m^2 (as we calculated earlier) and the area of the reservoir is 1.0 square meter.
Force = 250,000 N/m^2 x 1.0 m^2
Force = 250,000 Newtons
Therefore, the minimum force that must be exerted by the air compressor to lift the sedan is 250,000 Newtons.