A hydraulic lift is used to lift a heavy machine that is pushing down on a 3.0 m2 piston A1 with a force F1 of 1200 N. What force F2 needs to be exerted on a 0.090 m2 piston A2 to lift the machine? im having problems tring to solve it can you please help me?

The pressure (force/area) is the same in the system.

F1/A1=F2/A2

F2=F1*A2/A1=1200N*.090/3.0=400*.09=36N

Of course! I'd be happy to help you solve this problem.

To solve for the force F2 exerted on piston A2, we can use Pascal's law, which states that pressure is transmitted equally in all directions within a fluid. This means that the pressure exerted on piston A1 is equal to the pressure exerted on piston A2.

The formula to calculate pressure is:

Pressure = Force / Area

We already know the force exerted on piston A1 (F1 = 1200 N) and its area (A1 = 3.0 m²). We need to find the force exerted on piston A2 (F2) and its area (A2 = 0.090 m²).

Step 1: Calculate the pressure exerted on piston A1.
Pressure1 = F1 / A1

Step 2: Use Pascal's law to equate the pressures on both pistons.
Pressure1 = Pressure2

Step 3: Substitute the expressions for pressure into the equation.
F1 / A1 = F2 / A2

Step 4: Rearrange the equation to solve for F2.
F2 = (F1 / A1) * A2

Now, let's plug in the given values and solve for F2.

F2 = (1200 N / 3.0 m²) * 0.090 m²
F2 = (400 N/m²) * 0.090 m²
F2 = 36 N

Therefore, the force F2 that needs to be exerted on piston A2 to lift the machine is 36 Newtons.