If the 10-kg ball has a speed of 3 m/sec when it is at the position A, determine the tension in the cord and the rate of increase in speed of the ball at this position. Note that the ball is moving around a circular path in the vertical plane. **Pendulum Motion Analysis**In the study of pendulum motion, the diagram provided illustrates a simple pendulum setup. The pendulum consists of a mass (bob) A, attached to a string of length \(2 \, \text{m}\), which is fixed at point \(O\).**Key Components and Annotations:**1. **String Length**: The length of the string from \(O\) to the mass \(A\) is \(2 \, \text{m}\).2. **Angle (\(\theta\))**: The pendulum makes an angle \(\theta = 45^\circ\) with the vertical.3. **Velocity of the Bob**: At the position shown, the mass \(A\) is moving with a velocity of \(3 \, \text{m/s}\).4. **Gravitational Acceleration**: The acceleration due to gravity, \(g\), is taken as \(9.81 \, \text{m/s}^2\).The diagram also indicates the direction of gravitational force with a downward arrow and the respective value of \(g\).**Explanation for Educational Purposes:**- **Position and Angle**: The pendulum is currently displaced at an angle of \(45^\circ\) from its vertical rest position.- **Bob's Velocity**: The mass at point \(A\) is moving with a speed of \(3 \, \text{m/s}\), which is tangential to its circular path.- **String Length**: The length of the string remains constant at \(2 \, \text{m}\), which allows us to determine the potential energy and kinetic energy at point \(A\).Understanding the forces acting on the pendulum, along with its kinetic and potential energy at different points of its swing, provides fundamental insights into the principles of conservation of energy and harmonic motion.

Name: If the 10-kg ball has a speed of 3 m/sec when it is at the position A,
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: If the 10-kg ball has a speed of 3 m/sec when it is at the position A, determine the tension in the cord and the rate of increase in speed of the ball at this position. Note that the ball is moving around a circular path in the vertical plane. **Pend