In the figure, a package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle p = 49.4° with the horizontal; cord 2 is at angle 0. (a) For what value of 0 is the tension in cord 2 minimized? (b) What is the rat of the minimum tension in cord 2 to the weight of the package?

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Chapter1: Units, Trigonometry. And Vectors
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In the figure, a package of mass \( m \) hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at an angle \( \phi = 49.4^\circ \) with the horizontal; cord 2 is at an angle \( \theta \).

**Questions:**
(a) For what value of \( \theta \) is the tension in cord 2 minimized?
(b) What is the ratio of the minimum tension in cord 2 to the weight of the package?

**Diagram Explanation:**

- The diagram shows a setup where two cords are used to suspend a package. 
- Cord 1 is attached to the wall at an angle \( \phi = 49.4^\circ \) from the horizontal.
- Cord 2 is attached to the ceiling, making an angle \( \theta \) with the vertical direction.
- The package is suspended from the intersection point of these two cords.

This setup is used to analyze the physics of tension in the cords and their relation to the weight of the suspended package. The goal is to find the optimal angle \( \theta \) for minimizing tension in cord 2 and to calculate the corresponding tension ratio.
Transcribed Image Text:In the figure, a package of mass \( m \) hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at an angle \( \phi = 49.4^\circ \) with the horizontal; cord 2 is at an angle \( \theta \). **Questions:** (a) For what value of \( \theta \) is the tension in cord 2 minimized? (b) What is the ratio of the minimum tension in cord 2 to the weight of the package? **Diagram Explanation:** - The diagram shows a setup where two cords are used to suspend a package. - Cord 1 is attached to the wall at an angle \( \phi = 49.4^\circ \) from the horizontal. - Cord 2 is attached to the ceiling, making an angle \( \theta \) with the vertical direction. - The package is suspended from the intersection point of these two cords. This setup is used to analyze the physics of tension in the cords and their relation to the weight of the suspended package. The goal is to find the optimal angle \( \theta \) for minimizing tension in cord 2 and to calculate the corresponding tension ratio.
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