The object shown below (length = 6 m) remains completely stationary, despite the fact that three forces act on it. Forces 1 and 3 act at either end, while force 2 acts 1/4 of the way from the left end. new-torque-prob If the size of force 3 is 4 N, then how large must the other two forces be? F1 = F2 = N

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Chapter1: Units, Trigonometry. And Vectors
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**Equilibrium and Torque Problem**

The object shown (length = 6 m) remains completely stationary, despite the fact that three forces act on it. Forces \( F_1 \) and \( F_3 \) act at either end, while force \( F_2 \) acts \( \frac{1}{4} \) of the way from the left end.

**Diagram Explanation:**

- The object is depicted as a horizontal bar.
- Force \( F_1 \) is directed upward at the left end of the bar.
- Force \( F_3 \) is directed upward at the right end.
- Force \( F_2 \) is directed downward, located one-quarter of the length (1.5 meters) from the left end.

**Problem Statement:**

If the size of force \( F_3 \) is 4 N, calculate the magnitudes of forces \( F_1 \) and \( F_2 \).

- \( F_1 = \_\_\_ \) N
- \( F_2 = \_\_\_ \) N

Use the principles of equilibrium (net force and net torque equal zero) to solve for \( F_1 \) and \( F_2 \).
Transcribed Image Text:**Equilibrium and Torque Problem** The object shown (length = 6 m) remains completely stationary, despite the fact that three forces act on it. Forces \( F_1 \) and \( F_3 \) act at either end, while force \( F_2 \) acts \( \frac{1}{4} \) of the way from the left end. **Diagram Explanation:** - The object is depicted as a horizontal bar. - Force \( F_1 \) is directed upward at the left end of the bar. - Force \( F_3 \) is directed upward at the right end. - Force \( F_2 \) is directed downward, located one-quarter of the length (1.5 meters) from the left end. **Problem Statement:** If the size of force \( F_3 \) is 4 N, calculate the magnitudes of forces \( F_1 \) and \( F_2 \). - \( F_1 = \_\_\_ \) N - \( F_2 = \_\_\_ \) N Use the principles of equilibrium (net force and net torque equal zero) to solve for \( F_1 \) and \( F_2 \).
Below is a diagram of a baseball/forearm system at rest. It is acted on by four different forces: the weight of the forearm, the weight of the baseball, the bicep force, and a force from the upper arm bone (attached at the elbow).

### Diagram Explanation
The diagram shows a forearm at rest, holding a baseball. Key features include:
- **F_bicep**: The upward force exerted by the bicep.
- **M_forearm*g**: Downward force due to the weight of the forearm.
- **M_baseball*g**: Downward force due to the weight of the baseball.
- **Elbow as pivot**: The point around which the forearm rotates.

### Use the following values:
- Length of forearm, \( L = 18 \) cm
- Elbow to bicep distance, \( d = 2 \) cm
- Mass of forearm, \( M = 4 \) kg
- Mass of baseball, \( m = 2 \) kg

---

### Questions

a.) Based on torque considerations, the force of the bicep must be ___ the combined weight of the baseball/forearm.  
*(Make sure you understand the reasoning.)*

b.) How large is the force exerted by the bicep?

- Answer in Newtons (N)

c.) The upper arm bone exerts a force (not shown above) on the forearm. This force must be:

- Size: ___ N, direction: ___
  - Options for direction: upwards, downwards, to the left, to the right, none of these

---

### Submission
- Complete the selections and fill in the required values, then submit your answer.
Transcribed Image Text:Below is a diagram of a baseball/forearm system at rest. It is acted on by four different forces: the weight of the forearm, the weight of the baseball, the bicep force, and a force from the upper arm bone (attached at the elbow). ### Diagram Explanation The diagram shows a forearm at rest, holding a baseball. Key features include: - **F_bicep**: The upward force exerted by the bicep. - **M_forearm*g**: Downward force due to the weight of the forearm. - **M_baseball*g**: Downward force due to the weight of the baseball. - **Elbow as pivot**: The point around which the forearm rotates. ### Use the following values: - Length of forearm, \( L = 18 \) cm - Elbow to bicep distance, \( d = 2 \) cm - Mass of forearm, \( M = 4 \) kg - Mass of baseball, \( m = 2 \) kg --- ### Questions a.) Based on torque considerations, the force of the bicep must be ___ the combined weight of the baseball/forearm. *(Make sure you understand the reasoning.)* b.) How large is the force exerted by the bicep? - Answer in Newtons (N) c.) The upper arm bone exerts a force (not shown above) on the forearm. This force must be: - Size: ___ N, direction: ___ - Options for direction: upwards, downwards, to the left, to the right, none of these --- ### Submission - Complete the selections and fill in the required values, then submit your answer.
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