### Physics Problem: Collision and Spring Compression#### Given:- A ball of clay with mass \( \frac{M}{8} \).A larger mass, known as \( M \), is attached to a spring with spring constant \( k \). A ball of clay with mass \( \frac{M}{8} \) moves with speed \( v \) towards the larger mass \( M \). Upon collision, the ball of clay sticks to the larger mass, which was initially at rest. ##### Questions:a) What would be the speed of the combination after the collision?b) How much did the spring compress?c) How long did it take for the spring to be compressed due to the collision?#### Diagram Explanation:The diagram below provides a visual representation of the problem setup:- There is a ball of clay labeled \( \frac{M}{8} \) on the left, moving to the right with velocity \( v \).- In the middle, there is a larger mass \( M \) initially at rest.- The mass \( M \) is connected to a spring on the right side, which is fixed to a wall.- The spring has a spring constant \( k \).![Diagram](https://example.com/diagram-url)The diagram represents the initial positions and velocities before the collision.#### Analysis:To solve the given problems, we shall use the principles of conservation of momentum, spring compression, and kinematics.##### a) Speed of the CombinationWe'll use the conservation of momentum to find the speed of the combined mass after the collision.##### b) Spring CompressionWe'll use the conservation of energy to determine how much the spring compresses.##### c) Time for Spring CompressionTo find the time taken for the spring to compress, we shall analyze the simple harmonic motion caused by the spring.This problem touches on key concepts in mechanics, including collisions, momentum, and harmonic motion, making it an excellent example for educational purposes.

Name: ### Physics Problem: Collision and Spring Compression#### Given:- A b
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: ### Physics Problem: Collision and Spring Compression#### Given:- A ball of clay with mass \( \frac{M}{8} \).A larger mass, known as \( M \), is attached to a spring with spring constant \( k \). A ball of clay with mass \( \frac{M}{8} \) moves with