The 9.0 kg sphere A is held at an angle of 60° as shown, and then is released from rest and hits the B sphere which has a mass of 4.5 kg. In this crash the coefficient of restitution is e = 0.75. The sphere B is attached to the end of a rod lightweight rotating around the O point. The spring is initially non elongated and it is known that the maximum angle θ that the rod turned after the crash measured from the initial position was of 21.4º. Calculate:a) The speed with which sphere A impacts with sphere B. b) The magnitude and direction of the velocities of each sphere A and B after impact. c) The mechanical energy dissipated on impact. d) The spring stiffness constant k. The image is a diagram depicting a mechanical system involving a spring, a rod, and masses positioned in a vertical plane.### Description of the Diagram:1. **Spring and Rod System:** - A spring labeled "k" is horizontally positioned at an angle, connected at point "O" on the left side. The spring runs diagonally upward to connect with a vertical rod.2. **Points and Measurements:** - **Point A:** - Connected with a dashed line to the top of the vertical support and extends downward. - The length of this section from the top support to Point A is 450 mm. - It hangs making a 60° angle with the vertical line. - **Point B:** - Located further down from the vertical support and attached to a rod that has flexibility, indicating movement or rotation. - The rod connected to Point B measures 600 mm in length. - The angle between the rod and the horizontal line is labeled as θ (theta). 3. **Base Length:** - The horizontal distance separating the two anchor points at the base is labeled as 600 mm.### Explanation:- **Functionality:** The system potentially illustrates a scenario involving oscillation or vibration, wherein forces acting upon masses A and B cause the spring to compress or stretch, and the angle θ changes with movement.- **Applications:** This type of mechanical arrangement can be used for studying dynamics, harmonic motion, and stability in mechanical systems.- **Use in Education:** Such diagrams help students understand principles of mechanics, particularly the relationship between forces, angles, and motion in pendulum-like structures, as well as energy conservation in springs and lever systems. This type of illustration is beneficial in teaching modules focusing on mechanical dynamics, physics of motion, and engineering mechanics, helping visualize real-world applications of theoretical concepts.

GIVEN: * 9.0 kg sphere A *angle of 60° *4.5 kg sphere B *coefficient of restitution is e = 0.75 *…

Answered: The 9.0 kg sphere A is held at an angle…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The 9.0 kg sphere A is held at an angle of 60° as shown, and then is released from rest and hits the B sphere which has a mass of 4.5 kg. In this crash the coefficient of restitution is e = 0.75. The sphere B is attached to the end of a rod lightweight rotating around the O point. The spring is initially non elongated and it is known that the maximum angle θ that the rod turned after the crash measured from the initial position was of 21.4º. Calculate:

a) The speed with which sphere A impacts with sphere B.
b) The magnitude and direction of the velocities of each sphere A and B after impact.
c) The mechanical energy dissipated on impact.
d) The spring stiffness constant k.

The image is a diagram depicting a mechanical system involving a spring, a rod, and masses positioned in a vertical plane.

### Description of the Diagram:

1. **Spring and Rod System:**
- A spring labeled "k" is horizontally positioned at an angle, connected at point "O" on the left side. The spring runs diagonally upward to connect with a vertical rod.

2. **Points and Measurements:**
- **Point A:**
- Connected with a dashed line to the top of the vertical support and extends downward.
- The length of this section from the top support to Point A is 450 mm.
- It hangs making a 60° angle with the vertical line.
- **Point B:**
- Located further down from the vertical support and attached to a rod that has flexibility, indicating movement or rotation.
- The rod connected to Point B measures 600 mm in length.
- The angle between the rod and the horizontal line is labeled as θ (theta).

3. **Base Length:**
- The horizontal distance separating the two anchor points at the base is labeled as 600 mm.

### Explanation:

- **Functionality:**
The system potentially illustrates a scenario involving oscillation or vibration, wherein forces acting upon masses A and B cause the spring to compress or stretch, and the angle θ changes with movement.

- **Applications:**
This type of mechanical arrangement can be used for studying dynamics, harmonic motion, and stability in mechanical systems.

- **Use in Education:**
Such diagrams help students understand principles of mechanics, particularly the relationship between forces, angles, and motion in pendulum-like structures, as well as energy conservation in springs and lever systems.

This type of illustration is beneficial in teaching modules focusing on mechanical dynamics, physics of motion, and engineering mechanics, helping visualize real-world applications of theoretical concepts.

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