### ProblemConsider a slider, modeled as a particle \( P \) of mass \( m \), moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is \( v \), and the spring is stretched to length \( r > l_0 \), where \( l_0 \) is its unstretched length. The spring forms an angle \( \theta \) as shown, and the spring constant is \( k \).**Objective:**Solve for (a) the rates of change \( \dot{v} \) and \( \dot{\theta} \), and (b) the normal force the shaft applies to the collar.### Diagram ExplanationThe diagram consists of a mechanical setup showing:- **P**: The slider, shown as a yellow rectangle with a point indicating position on the shaft. It moves vertically along the shaft.- **Spring**: It is attached to the slider and forms an angle \( \theta \) with a reference horizontal line from point **O**.- **Force Indicator \( v \)**: An arrow pointing downwards from the slider, indicating the speed of movement along the shaft.- **Coordinates**: - \( r \): The stretched length of the spring from \( O \) to \( P \). - \( \theta \): The angle formed by the spring with the horizontal. The setup is labeled as "Motion in horizontal plane," highlighting that the entire system operates without gravitational influences.

Given:No radial acceleration, No angular acceleration, To find:(aT rate of change of velocity and…

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r>lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant is k. Solve for (a) the rates of change and é, and (b) the normal force the shaft applies to the collar.

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r>lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant is k. Solve for (a) the rates of change and é, and (b) the normal force the shaft applies to the collar.

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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Question

### Problem

Consider a slider, modeled as a particle \( P \) of mass \( m \), moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is \( v \), and the spring is stretched to length \( r > l_0 \), where \( l_0 \) is its unstretched length. The spring forms an angle \( \theta \) as shown, and the spring constant is \( k \).

**Objective:**

Solve for (a) the rates of change \( \dot{v} \) and \( \dot{\theta} \), and (b) the normal force the shaft applies to the collar.

### Diagram Explanation

The diagram consists of a mechanical setup showing:

- **P**: The slider, shown as a yellow rectangle with a point indicating position on the shaft. It moves vertically along the shaft.
- **Spring**: It is attached to the slider and forms an angle \( \theta \) with a reference horizontal line from point **O**.
- **Force Indicator \( v \)**: An arrow pointing downwards from the slider, indicating the speed of movement along the shaft.
- **Coordinates**:
- \( r \): The stretched length of the spring from \( O \) to \( P \).
- \( \theta \): The angle formed by the spring with the horizontal.

The setup is labeled as "Motion in horizontal plane," highlighting that the entire system operates without gravitational influences.

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