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Some shape with mass m is connected on the end of string of length L and spinning with angular speed ω on a smooth, coned surface. The opening angle of the cone is α. 1. What is the linear velocity of the body? 2. What is the reaction of the conical surface on the body? Find an algebraic expression for N in terms of the parameters of the problem and use it to evaluate your results for L = 5 m, m = 5 kg and α = 60 degrees (sin α = sqrt(3)/2, cos α = 1/2) 3. What should the angular velocity be to reduce the cone’s reaction to zero?

Some shape with mass m is connected on the end of string of length L and spinning with angular speed ω on a smooth, coned surface. The opening angle of the cone is α. 1. What is the linear velocity of the body? 2. What is the reaction of the conical surface on the body? Find an algebraic expression for N in terms of the parameters of the problem and use it to evaluate your results for L = 5 m, m = 5 kg and α = 60 degrees (sin α = sqrt(3)/2, cos α = 1/2) 3. What should the angular velocity be to reduce the cone’s reaction to zero?

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Some shape with mass m is connected on the end of string of length L and
spinning with angular speed ω on a smooth, coned surface. The opening angle of the cone is α.

1. What is the linear velocity of the body?

2. What is the reaction of the conical surface on the body? Find an algebraic expression for N in terms of the parameters of the problem and use it to evaluate your results for L = 5 m,
m = 5 kg and α = 60 degrees (sin α = sqrt(3)/2, cos α = 1/2)

3. What should the angular velocity be to reduce the cone’s reaction to zero?

The image depicts a conical pendulum. It consists of a mass \(m\) attached to the end of a string of length \(L\). The string forms an angle \(\alpha\) with the vertical axis of the cone. The pendulum is swinging in a horizontal circular motion, as indicated by the angular velocity \(\omega\). ### Diagram Explanation: - **Mass (\(m\))**: Represents the weight at the end of the pendulum. - **String Length (\(L\))**: The length of the string from the pivot point to the mass. - **Angle (\(\alpha\))**: The angle between the string and the vertical axis. - **Angular Velocity (\(\omega\))**: The rate of rotation of the mass around the central vertical axis. The diagram illustrates the concept of a conical pendulum, where the mass moves in a circular path while maintaining a constant angle with the vertical axis, combining principles of circular motion and gravity.
Transcribed Image Text:The image depicts a conical pendulum. It consists of a mass \(m\) attached to the end of a string of length \(L\). The string forms an angle \(\alpha\) with the vertical axis of the cone. The pendulum is swinging in a horizontal circular motion, as indicated by the angular velocity \(\omega\). ### Diagram Explanation: - **Mass (\(m\))**: Represents the weight at the end of the pendulum. - **String Length (\(L\))**: The length of the string from the pivot point to the mass. - **Angle (\(\alpha\))**: The angle between the string and the vertical axis. - **Angular Velocity (\(\omega\))**: The rate of rotation of the mass around the central vertical axis. The diagram illustrates the concept of a conical pendulum, where the mass moves in a circular path while maintaining a constant angle with the vertical axis, combining principles of circular motion and gravity.
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