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------------------------------------------------ Given:

- [tex]F_1 = 25 \, \text{N}[/tex]
- [tex]A_1 = 10 \, \text{cm}^2[/tex]
- [tex]A_2 = 60 \, \text{cm}^2[/tex]

Find [tex]F_2[/tex].

To solve this problem, we'll use Pascal's Principle, which is often applied in hydraulic systems. This principle states that pressure applied at one point in an incompressible fluid is transmitted equally in all directions throughout the fluid.

The formula to calculate the force in a hydraulic system is given by:

[tex]\frac{F_1}{A_1} = \frac{F_2}{A_2}[/tex]
Where:

[tex]F_1[/tex] is the force applied to the first piston,
[tex]A_1[/tex] is the area of the first piston,
[tex]F_2[/tex] is the force applied to the second piston,
[tex]A_2[/tex] is the area of the second piston.

Given:

[tex]F_1 = 25 \text{ N}[/tex]
[tex]A_1 = 10 \text{ cm}^2[/tex]
[tex]A_2 = 60 \text{ cm}^2[/tex]

We want to find [tex]F_2[/tex].

Rearranging the formula to solve for [tex]F_2[/tex], we get:

[tex]F_2 = \frac{A_2}{A_1} \times F_1[/tex]

Substitute the given values:

[tex]F_2 = \frac{60}{10} \times 25[/tex]

Calculate:
[tex]F_2 = 6 \times 25 = 150 \text{ N}[/tex]

So, the force [tex]F_2[/tex] applied to the second piston is 150 N.