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.)
   

pressure in the oil is the same on both sides

p *.1 = 25,000
p = 250,000N/m^2
F = p*A = 250,000 *1 = 250,000 N

To find the minimum force exerted by the air compressor, we can use Pascal's Law, which states that pressure is transmitted equally in all directions in a confined fluid.

First, let's calculate the pressure exerted by the weight of the sedan on the piston. The formula to calculate pressure is:

Pressure = Force / Area

The force in this case is the weight of the sedan, which is 25,000 Newtons. The area of the piston is given as 0.1 square meters. Substituting the values into the formula, we get:

Pressure = 25,000 N / 0.1 m²

Simplifying the expression, we find that the pressure exerted by the sedan on the piston is 250,000 Pascal (Pa).

Since the pressure is transmitted equally in all directions, the pressure exerted by the oil in the reservoir will also be 250,000 Pa.

To find the force exerted by the air compressor, we can again use the formula for pressure:

Pressure = Force / Area

The pressure is 250,000 Pa, and the area of the reservoir is given as 1.0 square meter. Substituting the values into the formula, we can solve for the force:

250,000 Pa = Force / 1.0 m²

Rearranging the equation, we find that the force exerted by the air compressor is 250,000 Newtons.

Therefore, the minimum force that must be exerted by the air compressor to lift the sedan is 250,000 Newtons.