Review Constans (Figure 1)A bob of mass m is suspended from a fixed point with a massless string of length L (i.e., it is a pendulum). You are to investigate the motion in which the Part A string moves in a cone with half-angle 0 moves in a horizontal circle with the string always making an angle 0 What tangential speed, v, must the bob have so that from the vertical? Express your answer in terms of some or all of the variables m, L, and 0, as well as the free-fall acceleration g. • View Available Hint(s) ην ΑΣφ v = Submit Part B Figure < 1 of 1 > How long does it take the bob to make one full revolution (one complete trip around the circle)? Express your answer in terms of some or all of the variables m, L, and 0, as well as the free-fall acceleration q. • View Available Hint(s) ? Submit

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**Pendulum Motion in a Conical Path**

**Introduction:**
A bob of mass \( m \) is suspended from a fixed point with a massless string of length \( L \) (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle \( \theta \).

**Figure Explanation:**
The diagram shows a pendulum consisting of a bob of mass \( m \) suspended by a string of length \( L \). The string makes a conical path as it swings, with the angle \( \theta \) between the string and the vertical axis. The bob moves with a tangential speed \( v \) in a horizontal circle.

**Problem Statements:**

**Part A:**
What tangential speed, \( v \), must the bob have so that it moves in a horizontal circle with the string always making an angle \( \theta \) from the vertical?

- **Expression Required:** Express your answer in terms of some or all of the variables \( m \), \( L \), and \( \theta \), as well as the free-fall acceleration \( g \).
- **Response Box:** Provide your answer in the space provided. Use the available hint if necessary.

**Part B:**
How long does it take the bob to make one full revolution (one complete trip around the circle)?

- **Expression Required:** Express your answer in terms of some or all of the variables \( m \), \( L \), and \( \theta \), as well as the free-fall acceleration \( g \).
- **Response Box:** Provide your answer in the space provided. Use the available hint if necessary.

Students are encouraged to apply concepts of circular motion and dynamics to solve these problems and submit their responses for feedback.
Transcribed Image Text:**Pendulum Motion in a Conical Path** **Introduction:** A bob of mass \( m \) is suspended from a fixed point with a massless string of length \( L \) (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle \( \theta \). **Figure Explanation:** The diagram shows a pendulum consisting of a bob of mass \( m \) suspended by a string of length \( L \). The string makes a conical path as it swings, with the angle \( \theta \) between the string and the vertical axis. The bob moves with a tangential speed \( v \) in a horizontal circle. **Problem Statements:** **Part A:** What tangential speed, \( v \), must the bob have so that it moves in a horizontal circle with the string always making an angle \( \theta \) from the vertical? - **Expression Required:** Express your answer in terms of some or all of the variables \( m \), \( L \), and \( \theta \), as well as the free-fall acceleration \( g \). - **Response Box:** Provide your answer in the space provided. Use the available hint if necessary. **Part B:** How long does it take the bob to make one full revolution (one complete trip around the circle)? - **Expression Required:** Express your answer in terms of some or all of the variables \( m \), \( L \), and \( \theta \), as well as the free-fall acceleration \( g \). - **Response Box:** Provide your answer in the space provided. Use the available hint if necessary. Students are encouraged to apply concepts of circular motion and dynamics to solve these problems and submit their responses for feedback.
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