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To calculate the reaction forces in the beam, we need to apply static equilibrium principles. From the diagram and given information, the beam is supported at two points: Point A (a pinned support) and Point B (a roller). There are two external forces acting on the beam: 20N and 30N, spaced 1 meter and 2 meters apart from each other.

For a beam to be in equilibrium, the following conditions must hold:
1. The sum of all vertical forces must be zero: \( \sum F_y = 0 \).
2. The sum of all moments about any point must be zero: \( \sum M = 0 \).

Let’s define the forces at the supports as:
- \( R_A \): Reaction at point A (vertical force).
- \( R_B \): Reaction at point B (vertical force).

### Step 1: Moment about point A
Taking moments about point A (to eliminate \( R_A \)):
\[
\sum M_A = 0 \implies R_B \times 3\,\text{m} - 30\,\text{N} \times 2\,\text{m} - 20\,\text{N} \times 1\,\text{m} = 0
\]
\[
3R_B = 60 + 20 = 80
\]
\[
R_B = \frac{80}{3} \approx 26.67\,\text{N}
\]

### Step 2: Vertical equilibrium
Now, using the condition that the sum of vertical forces must be zero:
\[
R_A + R_B = 20\,\text{N} + 30\,\text{N} = 50\,\text{N}
\]
\[
R_A = 50 - 26.67 = 23.33\,\text{N}
\]

### Final Answer:
- Reaction at Point A, \( R_A = 23.33\,\text{N} \)
- Reaction at Point B, \( R_B = 26.67\,\text{N} \)

Would you like more details or have any questions on these calculations?

Here are 5 related questions to expand the topic:
1. How would the reaction forces change if the load positions were altered?
2. What would be the effect if point A were a roller and point B were pinned?
3. How does the presence of a moment affect the reaction forces in a beam?
4. What if an additional horizontal force was applied to the beam at point A—how would you calculate the reactions?
5. How do we apply equilibrium equations to a beam with more than two supports?

**Tip:** When solving for reactions in beams, always start with the moment equation to eliminate one unknown, making the process simpler.

Calculate the reaction force in the beam. Note that point A is a pinned support and point B is a roller.

Learn how to calculate the reaction forces in a beam supported at Point A (pinned) and Point B (roller). The problem includes balancing vertical forces and moments to determine the reaction forces using static equilibrium principles. Suitable for high school students in Grades 10-12.

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