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 that must be exerted by the air compressor, we can use Pascal's Law, which states that the pressure exerted on a fluid is transmitted equally in all directions.
First, we need to calculate the pressure exerted on the sedan by its weight. The weight of the sedan is given as 25,000 Newtons.
Pressure = Force / Area
The area in this case is the cross-sectional area of the piston, which is 0.1 square meters.
Pressure = 25,000 N / 0.1 m² = 250,000 Pa
Now, using Pascal's Law, we know that the pressure exerted by the air compressor on the oil in the reservoir will be the same as the pressure under the sedan. Since the cross-sectional area of the reservoir is given as 1.0 square meter, the force exerted by the air compressor can be calculated using the following formula:
Force = Pressure × Area
Force = 250,000 Pa × 1.0 m² = 250,000 N
Therefore, the minimum force that must be exerted by the air compressor is 250,000 Newtons.