Certainly! Let's solve the problem step by step.
To determine the force in a hydraulic system, we need to consider the relationship between pressure, area, and force.
The correct formula to calculate the force ([tex]\( F \)[/tex]) in a hydraulic system is given by:
[tex]\[ F = P \times A \][/tex]
where:
- [tex]\( F \)[/tex] is the force.
- [tex]\( P \)[/tex] is the pressure.
- [tex]\( A \)[/tex] is the area.
This formula expresses that the force exerted by a hydraulic system is directly proportional to the pressure applied and the area through which the force is being applied.
Now, let's examine the given choices:
1. [tex]\( F = P - A \)[/tex]
2. [tex]\( F = P / A \)[/tex]
3. [tex]\( F = P + A \)[/tex]
4. [tex]\( F = P \times A \)[/tex]
- Option 1 ([tex]\( F = P - A \)[/tex]) is incorrect because force is not calculated by subtracting area from pressure.
- Option 2 ([tex]\( F = P / A \)[/tex]) is incorrect because dividing pressure by area does not give force.
- Option 3 ([tex]\( F = P + A \)[/tex]) is incorrect because adding pressure and area does not yield force.
- Option 4 ([tex]\( F = P \times A \)[/tex]) is correct because it matches the established formula for calculating the force in a hydraulic system.
Therefore, the correct equation to determine the force in a hydraulic system is:
[tex]\[ F = P \times A \][/tex]
So, the correct choice is:
[tex]\[ \boxed{4} \][/tex]
