https://file.aiquickdraw.com/mathbot/file/1726317530396xxi7o387.jpg

Let's break down the problem in parts based on the images.

### For **Gambar 1**:
We are given five forces of \(1000 \, \text{kg}\) each acting at different angles, and the task is to find the resultant force graphically. The scale provided is \(1 \, \text{cm} = 200 \, \text{kg}\). To find the resultant graphically, you can use a vector addition method, like the **polygon of forces**. 

Steps:
1. **Draw each force to scale**: 
   - Convert each force from kg to cm using the scale (since \(1 \, \text{cm} = 200 \, \text{kg}\)).
   - Draw the vectors with correct magnitude and direction.

2. **Apply head-to-tail method** to sum the vectors.

3. **Measure the resultant** (the distance from the tail of the first vector to the head of the last vector) and convert it back to kg using the scale.

### For **Gambar 2, 3, 4**:
These diagrams show systems of forces acting on a point. You are asked to compute the resultant analytically. This requires resolving each force into its components (horizontal and vertical) and then summing these components to find the resultant force.

The analytical method would follow these steps:
1. **Resolve each force into components**:
   \[
   F_x = F \cdot \cos(\theta) \quad \text{(horizontal component)}
   \]
   \[
   F_y = F \cdot \sin(\theta) \quad \text{(vertical component)}
   \]
   Where \(F\) is the magnitude of the force, and \(\theta\) is the angle with respect to the horizontal axis.

2. **Sum the components** for each direction:
   \[
   \Sigma F_x = F_{x1} + F_{x2} + \dots
   \]
   \[
   \Sigma F_y = F_{y1} + F_{y2} + \dots
   \]

3. **Compute the magnitude of the resultant force**:
   \[
   R = \sqrt{(\Sigma F_x)^2 + (\Sigma F_y)^2}
   \]

4. **Find the direction of the resultant**:
   \[
   \theta_R = \tan^{-1}\left(\frac{\Sigma F_y}{\Sigma F_x}\right)
   \]

For each of the figures (**Gambar 2, 3, and 4**), the same process applies, but the magnitudes and angles of the forces are different. Would you like to proceed with a specific figure first, or shall I compute one of the systems in more detail for you?

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### Five relative questions:
1. Would you like a step-by-step solution for any specific diagram (Gambar 2, 3, or 4)?
2. Do you need help with the graphical vector addition for Gambar 1?
3. Would you like to go over how to resolve forces into components in detail?
4. Should we focus on the resultant magnitude or direction calculation next?
5. Are there any specific angles or forces you'd like clarified?

**Tip**: When resolving forces into components, always double-check the direction (positive or negative) based on the coordinate axes.

Determine the resultant force of five forces, each 1000 kg, working graphically (Figure 1). The scale is 1 cm = 200 kg. Also, compute the resultant forces of the systems in Figures 2, 3, and 4 using an analytical method.

Explore how to calculate the resultant force of multiple forces using both graphical and analytical methods. Learn the step-by-step process for resolving forces and applying vector addition, suitable for undergraduate physics and engineering students.

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