A ball is being rotated at the end of a 4-meter long string such that it is describing a circular path. If the angle that the string makes with the vertical is 40°, and the ball has a mass of 10-Kg, determine the speed of the ball and the tension in the string

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Chapter1: Units, Trigonometry. And Vectors
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A ball is being rotated at the end of a 4-meter long string such that it is describing a circular path. If the angle that the string makes with the vertical is 40°, and the ball has a mass of 10-Kg, determine the speed of the ball and the tension in the string

The provided image illustrates the dynamics of a pendulum in motion. The diagram features a spherical object attached to a string, depicting a pendulum's trajectory. Key elements of the diagram are outlined and explained below:

1. **Pendulum Construction**: 
   - **Mass (m)**: The bob at the end of the string is circular and labeled with "m" representing its mass. 
   - **String Length**: The string, which is depicted as a straight line, is labeled with a length of "4m" indicating that the pendulum's string is 4 meters long.
   
2. **Swing Angle**:
   - The string forms an angle of 40 degrees with the vertical axis when the pendulum swings to one side. This is clearly indicated by the angle notation "40°" drawn between the string and the dashed vertical line representing the equilibrium position of the pendulum.

3. **Trajectory**:
   - The dashed curve around the vertical axis shows the path of the pendulum bob during its swing. This demonstrates one possible position of the mass at its extremity during a cycle and emphasizes the motion of the pendulum.

This diagram illustrates a simple pendulum's setup and the basic principles of its motion, such as its length and angle of swing. This is essential for students learning about periodic motion, gravitational influences, and harmonic oscillations.
Transcribed Image Text:The provided image illustrates the dynamics of a pendulum in motion. The diagram features a spherical object attached to a string, depicting a pendulum's trajectory. Key elements of the diagram are outlined and explained below: 1. **Pendulum Construction**: - **Mass (m)**: The bob at the end of the string is circular and labeled with "m" representing its mass. - **String Length**: The string, which is depicted as a straight line, is labeled with a length of "4m" indicating that the pendulum's string is 4 meters long. 2. **Swing Angle**: - The string forms an angle of 40 degrees with the vertical axis when the pendulum swings to one side. This is clearly indicated by the angle notation "40°" drawn between the string and the dashed vertical line representing the equilibrium position of the pendulum. 3. **Trajectory**: - The dashed curve around the vertical axis shows the path of the pendulum bob during its swing. This demonstrates one possible position of the mass at its extremity during a cycle and emphasizes the motion of the pendulum. This diagram illustrates a simple pendulum's setup and the basic principles of its motion, such as its length and angle of swing. This is essential for students learning about periodic motion, gravitational influences, and harmonic oscillations.
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