https://file.aiquickdraw.com/mathbot/file/1726539087526ba48qius.jpg

The task in the image involves determining the resultant of several force systems using graphical and analytical methods. Let's break it down step-by-step:

### Task 1:
- **Problem:** Find the resultant of five forces, each of 1000 kg, working graphically as shown in **Gambar 1**.
- **Scale:** 1 cm = 200 kg.

You need to draw the forces to scale and use vector addition (head-to-tail method) to find the resultant force. Since each force is 1000 kg, each vector should be drawn as 5 cm (since \( \frac{1000 \, \text{kg}}{200 \, \text{kg/cm}} = 5 \, \text{cm} \)).

### Task 2:
- **Problem:** Calculate the resultant for the force systems shown in **Gambar 2, 3, and 4** analytically. This requires you to break each force into its horizontal and vertical components and then sum them to find the overall resultant vector.
    - **Gambar 2:** Forces are given with angles between them (50 kg, 40 kg, etc.) and their directions (like 40°, 90°, etc.).
    - **Gambar 3 & 4:** Larger forces (in the 1000 kg range) are depicted at various angles.

### To solve this:
1. **Resolve each force** into its horizontal and vertical components using:
   - Horizontal component: \( F_x = F \cos(\theta) \)
   - Vertical component: \( F_y = F \sin(\theta) \)
2. **Sum the components** in the x and y directions separately.
3. **Find the magnitude** of the resultant force using:
   \[
   R = \sqrt{(R_x^2 + R_y^2)}
   \]
4. **Find the angle** of the resultant using:
   \[
   \theta_R = \tan^{-1}\left(\frac{R_y}{R_x}\right)
   \]

Would you like assistance in solving a specific part or need help with the detailed steps? Let me know!

Here are 5 questions that might help expand on this topic:
1. What is the graphical method of vector addition, and how does it work?
2. How do you apply trigonometric functions to resolve forces into components?
3. How do you interpret the resultant vector direction from the components?
4. What are common mistakes in graphical vector addition, and how can they be avoided?
5. How can you verify the accuracy of your result in force vector problems?

**Tip:** Always double-check the angle directions when resolving forces into components. Misinterpreting the angle's quadrant can lead to errors in the resultant force calculation.

Determine the resultant of five forces each of 1000 kg working graphically (using vector addition) and analytically for different systems of forces as shown in the images.

Learn how to calculate the resultant force of multiple forces, both graphically and analytically, using trigonometry and vector addition. This example involves forces of up to 1000 kg and resolves them using fundamental physics concepts. Suitable for high school physics students.

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