Can someone walk me through this practice problem.  What is the normal force exerted on the board from support 2? and What is the normal force exerted on the board from support 1? My answer should be expressed in terms of M, m, and L

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Can someone walk me through this practice problem. 

What is the normal force exerted on the board from support 2? and What is the normal force exerted on the board from support 1? My answer should be expressed in terms of M, m, and L.

**Title: Understanding Torque and Balance with a Uniform Board**

**Introduction:**

In this scenario, we analyze the balance of a uniform board. The board has a mass \( M \) and length \( L \) and is supported horizontally by two triangular stands. A bear of mass \( m \) sits on the board. This setup demonstrates principles of torque and equilibrium.

**Diagram Explanation:**

The diagram features:

- **A horizontal board** with two supports: 
  - **Support 1** is located at the far left end of the board.
  - **Support 2** is placed at a distance of \( \frac{3L}{4} \) from the left end.
  
- **A bear** positioned on the board at \( \frac{L}{3} \) from the left end.

- **Two trees** on either side, symbolizing the passageway for woodland creatures.

**Physics Concepts:**

This setup is an example of static equilibrium. The board is in balance due to the torques around any pivot point summing to zero. The bear’s position influences the distribution of forces on the supports. Understanding this system helps in grasping concepts of:

- **Torque** (\( \tau \)), calculated by \( \tau = r \times F \), where \( r \) is the distance from the pivot, and \( F \) is the force.
- **Equilibrium**, where the sum of vertical forces and torques is zero.

**Applications:**

Such concepts are fundamental in engineering and physics, illustrating how forces and loads are managed in bridges and other structures.
Transcribed Image Text:**Title: Understanding Torque and Balance with a Uniform Board** **Introduction:** In this scenario, we analyze the balance of a uniform board. The board has a mass \( M \) and length \( L \) and is supported horizontally by two triangular stands. A bear of mass \( m \) sits on the board. This setup demonstrates principles of torque and equilibrium. **Diagram Explanation:** The diagram features: - **A horizontal board** with two supports: - **Support 1** is located at the far left end of the board. - **Support 2** is placed at a distance of \( \frac{3L}{4} \) from the left end. - **A bear** positioned on the board at \( \frac{L}{3} \) from the left end. - **Two trees** on either side, symbolizing the passageway for woodland creatures. **Physics Concepts:** This setup is an example of static equilibrium. The board is in balance due to the torques around any pivot point summing to zero. The bear’s position influences the distribution of forces on the supports. Understanding this system helps in grasping concepts of: - **Torque** (\( \tau \)), calculated by \( \tau = r \times F \), where \( r \) is the distance from the pivot, and \( F \) is the force. - **Equilibrium**, where the sum of vertical forces and torques is zero. **Applications:** Such concepts are fundamental in engineering and physics, illustrating how forces and loads are managed in bridges and other structures.
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