The image presents a physics problem involving a ball attached to one end of an ideal string with length \(L = 1.1 \, \text{m}\). The other end of the string is fixed, allowing the ball to move in a vertical circular path. The ball is initially given a speed \(v_0\) from point \(A\), where \(\theta = 27^\circ\). The task is to determine the smallest possible value of \(v_0\) required for the ball to reach point \(B\) while traveling along a circular arc with radius \(L\). The problem assumes there is no friction or air resistance.**Diagram Explanation:**- The diagram features a circular path marked with a dashed line, representing the trajectory of the ball, with the center of the circle below point \(A\).- Point \(A\) is where the ball starts, making an angle \(\theta\) with the vertical.- \(L\) is the radius of the circle and the length of the string.- \(v_0\) is the initial velocity of the ball at point \(A\), shown by an arrow pointing downward and tangentially to the circle.- Point \(B\) is located directly above the circle’s center, with velocity \(v\) pointing upwards. **Instructions:** \[ \text{Hint: Start by drawing a Free Body Diagram (FBD) of the ball at point B. Use Newton's second law to find the minimum speed at B and then use energy conservation to find the required minimum speed at A.} \]\[ v_0 = \_\_\_\_\_\_\_\, \text{m/s} \]

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Description: The image presents a physics problem involving a ball attached to one end of an ideal string with length \(L = 1.1 \, \text{m}\). The other end of the string is fixed, allowing the ball to move in a vertical circular path. The ball is initially give

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The figure shows a ball attached to one end of an ideal string of length L=1.1 m. The string's other end is held fixed as the ball is given an initial speed vo from point A where 0 = 27° on a vertical circle. Find the smallest possible value of vo if the ball at point B is traveling along a circular arc of radius L. Ignore friction and air resistance. A VO VO 0 V B [Hint: Start by drawing a FBD of the ball at point B. Use Newton's second law to find the minimum speed at B and then use energy conservation to find the required minimum speed at A.] m S ★ㅌㅁ 0 11:35 PM 10/31/2022 3

The figure shows a ball attached to one end of an ideal string of length L=1.1 m. The string's other end is held fixed as the ball is given an initial speed vo from point A where 0 = 27° on a vertical circle. Find the smallest possible value of vo if the ball at point B is traveling along a circular arc of radius L. Ignore friction and air resistance. A VO VO 0 V B [Hint: Start by drawing a FBD of the ball at point B. Use Newton's second law to find the minimum speed at B and then use energy conservation to find the required minimum speed at A.] m S ★ㅌㅁ 0 11:35 PM 10/31/2022 3

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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The image presents a physics problem involving a ball attached to one end of an ideal string with length \(L = 1.1 \, \text{m}\). The other end of the string is fixed, allowing the ball to move in a vertical circular path. The ball is initially given a speed \(v_0\) from point \(A\), where \(\theta = 27^\circ\). The task is to determine the smallest possible value of \(v_0\) required for the ball to reach point \(B\) while traveling along a circular arc with radius \(L\). The problem assumes there is no friction or air resistance.

**Diagram Explanation:**

- The diagram features a circular path marked with a dashed line, representing the trajectory of the ball, with the center of the circle below point \(A\).
- Point \(A\) is where the ball starts, making an angle \(\theta\) with the vertical.
- \(L\) is the radius of the circle and the length of the string.
- \(v_0\) is the initial velocity of the ball at point \(A\), shown by an arrow pointing downward and tangentially to the circle.
- Point \(B\) is located directly above the circle’s center, with velocity \(v\) pointing upwards.

**Instructions:**

\[ \text{Hint: Start by drawing a Free Body Diagram (FBD) of the ball at point B. Use Newton's second law to find the minimum speed at B and then use energy conservation to find the required minimum speed at A.} \]

\[ v_0 = \_\_\_\_\_\_\_\, \text{m/s} \]

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