Two construction workers carry a 2.8 m long wooden beam on their shoulders. It is horizontal while they carry it. One worker is at the end of the beam and the other is standing 2.6 m away from the first worker. The beam has a mass of 190 kg. a. Do the workers exert the same amount of force on the beam? You can just use intuition on this one. No math is required.

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### Problem Statement: Mechanics of Forces on a Beam

Two construction workers carry a 2.8 m long wooden beam on their shoulders. It is horizontal while they carry it. One worker is at the end of the beam and the other is standing 2.6 m away from the first worker. The beam has a mass of 190 kg.

**Questions:**

1. **Equilibrium of Forces:**
   a. Do the workers exert the same amount of force on the beam? You can just use intuition on this one. No math is required.

2. **Calculating Force Ratios:**
   a. What is the ratio of the force that each provides to hold the beam up (find \( \frac{F_1}{F_2} \))? Now you need some math.

3. **Balancing Additional Weight:**
   a. If a third worker with a mass of 70 kg sat on the beam, where would he or she have to sit in order for both construction workers carrying the beam to exert the same force? Report your answer from the end of the beam where the first worker is holding it.

**Detailed Explanation of Questions:**

- For question **1a**, consider the positions of the workers. The worker standing closer to the center is likely to bear more of the beam's weight. 

- For question **2a**, you need to use the principle of moments (torque). The total torque about any point (typically where one of the workers is standing) should be zero for the beam to be in equilibrium.

- For question **3a**, one would balance the moments considering the weight of the third worker and where they should sit such that the forces exerted by both construction workers are equal.

**If there were any diagrams or graphs:**

- **Diagram 1: Force Distribution on the Beam**
  - Includes positions of the workers and the distances.
  - Shows the forces \( F_1 \) and \( F_2 \) exerted by the two workers.

- **Graph 1: Equilibrium Force Calculation**
  - A plot illustrating force distribution for varying positions of additional weights if relevant.

This problem is a great way to understand how forces and torque work in practical settings and is applicable to many engineering fields.
Transcribed Image Text:### Problem Statement: Mechanics of Forces on a Beam Two construction workers carry a 2.8 m long wooden beam on their shoulders. It is horizontal while they carry it. One worker is at the end of the beam and the other is standing 2.6 m away from the first worker. The beam has a mass of 190 kg. **Questions:** 1. **Equilibrium of Forces:** a. Do the workers exert the same amount of force on the beam? You can just use intuition on this one. No math is required. 2. **Calculating Force Ratios:** a. What is the ratio of the force that each provides to hold the beam up (find \( \frac{F_1}{F_2} \))? Now you need some math. 3. **Balancing Additional Weight:** a. If a third worker with a mass of 70 kg sat on the beam, where would he or she have to sit in order for both construction workers carrying the beam to exert the same force? Report your answer from the end of the beam where the first worker is holding it. **Detailed Explanation of Questions:** - For question **1a**, consider the positions of the workers. The worker standing closer to the center is likely to bear more of the beam's weight. - For question **2a**, you need to use the principle of moments (torque). The total torque about any point (typically where one of the workers is standing) should be zero for the beam to be in equilibrium. - For question **3a**, one would balance the moments considering the weight of the third worker and where they should sit such that the forces exerted by both construction workers are equal. **If there were any diagrams or graphs:** - **Diagram 1: Force Distribution on the Beam** - Includes positions of the workers and the distances. - Shows the forces \( F_1 \) and \( F_2 \) exerted by the two workers. - **Graph 1: Equilibrium Force Calculation** - A plot illustrating force distribution for varying positions of additional weights if relevant. This problem is a great way to understand how forces and torque work in practical settings and is applicable to many engineering fields.
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