3. What are the conditions for equilibrium (words and equations)? Now, a force is applied to a rope that is connected to two other ropes as shown. Draw a free body diagram for the O-ring connecting all 3 ropes and use Newton's 1st Law to calculate the tensions in ropes 1 and 2. I

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**Question 3: Conditions for Equilibrium**

**Text:**

What are the conditions for equilibrium (words and equations)? Now, a force is applied to a rope that is connected to two other ropes as shown. Draw a free body diagram for the O-ring connecting all 3 ropes and use Newton’s 1st Law to calculate the tensions in ropes 1 and 2.

**Diagram Explanation:**

The diagram shows an O-ring at the center to which three ropes are attached. 

- **Rope 1** is horizontal to the left.
- **Rope 2** is vertical, heading upwards.
- **A force of 100 N** is applied to a third rope making a 30° angle with Rope 1 to the right.

Newton's First Law states that an object is in equilibrium when the sum of the forces acting on it is zero. This means that both the horizontal and vertical components of the forces must be balanced. 

To solve for the tensions in Rope 1 and Rope 2, you can use trigonometric functions to resolve the 100 N force into horizontal and vertical components and apply the equilibrium conditions:

- **Horizontal Equilibrium:** Tension in Rope 1 = Horizontal component of 100 N.
- **Vertical Equilibrium:** Tension in Rope 2 = Vertical component of 100 N.
Transcribed Image Text:**Question 3: Conditions for Equilibrium** **Text:** What are the conditions for equilibrium (words and equations)? Now, a force is applied to a rope that is connected to two other ropes as shown. Draw a free body diagram for the O-ring connecting all 3 ropes and use Newton’s 1st Law to calculate the tensions in ropes 1 and 2. **Diagram Explanation:** The diagram shows an O-ring at the center to which three ropes are attached. - **Rope 1** is horizontal to the left. - **Rope 2** is vertical, heading upwards. - **A force of 100 N** is applied to a third rope making a 30° angle with Rope 1 to the right. Newton's First Law states that an object is in equilibrium when the sum of the forces acting on it is zero. This means that both the horizontal and vertical components of the forces must be balanced. To solve for the tensions in Rope 1 and Rope 2, you can use trigonometric functions to resolve the 100 N force into horizontal and vertical components and apply the equilibrium conditions: - **Horizontal Equilibrium:** Tension in Rope 1 = Horizontal component of 100 N. - **Vertical Equilibrium:** Tension in Rope 2 = Vertical component of 100 N.
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