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Let's tackle this statics problem step by step:

### Part 1: **Resultant Force Calculation**
#### (b) Magnitude of the Resultant Force
The forces acting along the same line (horizontal) are given in terms of \(a\):

- \( P1 = a \, \text{kN} \)
- \( P2 = 3a \, \text{kN} \)
- \( P3 = 2a \, \text{kN} \)
- \( P4 = 3a \, \text{kN} \)
- \( P5 = 2a \, \text{kN} \)

The total resultant force \(R\) is the sum of all these forces:

\[
R = P1 + P2 + P3 + P4 + P5
\]

\[
R = a + 3a + 2a + 3a + 2a = 11

Given a static equilibrium problem where forces P1, P2, P3, P4, and P5 are applied at different heights along a vertical line, calculate the resultant force, determine the location of the resultant force, and find the centroid of a given cross-sectional shape.

Solve a statics problem involving multiple forces acting on a vertical line. Learn how to calculate the resultant force, determine its location, and find the centroid of a given cross-sectional area with dimensions. This problem covers key statics concepts, including moments and equilibrium.

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