### Problem 2/186: Hoisting System for Kayaks**Problem Statement:**The hoisting system shown is used to easily raise kayaks for overhead storage. Determine expressions for the upward velocity and acceleration of the kayak at any height \( y \) if the winch \( M \) reels in cable at a constant rate \( \dot{l} \). Assume that the kayak remains level.**Detailed Diagram Explanation:**The diagram illustrates a hoisting system for lifting a kayak overhead. The system comprises:1. **Winch (M):** Positioned on the left side, the winch is responsible for reeling in the cable.2. **Pulleys:** There are multiple pulleys arranged to distribute the cable as follows: - One pulley at each end of the overhead beam. - One pulley in the center of the beam.3. **Cable Path:** The cable runs from the winch through the pulleys, lifting the kayak from points A (near the front) and B (near the back) evenly.4. **Kayak:** The kayak is horizontally positioned, ensuring it remains level when lifted.5. **Distance Labels:** - \( b \): The horizontal distance between each pulley. - \( y \): Vertical distance from the kayak to the overhead beam.**Detailed Steps for Solution:**1. **Understanding the Cable Mechanics:** - As the winch (\( M \)) reels in the cable at a constant rate \( \dot{l} \), it shortens the total length of the cable in the system. - The length \( l \) corresponds to the combined lengths of cable segments passing through pulleys and hoisting the kayak.2. **Velocity and Acceleration Relationships:** - Since the winch reels at a constant rate, \( \dot{l} \) is constant. - The vertical speed \( (V_y) \) and acceleration \( (a_y) \) of the kayak are tied to the rate at which the cable is reeled in.These factors ensure a systematic approach to determining the expressions for the upward velocity and acceleration of the kayak as it is hoisted.This hoisting system allows for efficient storage of kayaks by leveraging mechanical advantage, ensuring that the kayak remains level and stable during the lifting process. This is crucial for preserving the integrity of the stored kayak and ensuring user safety.

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2/186 The hoisting system shown is used to easily raise kayaks for overhead storage. Determine expressions for the upward velocity and acceleration of the kayak at any height y if the winch M reels in cable at a constant rate ¡ . As- sume that the kayak remains level. -b b y M A b PROBLEM 2/186 B

2/186 The hoisting system shown is used to easily raise kayaks for overhead storage. Determine expressions for the upward velocity and acceleration of the kayak at any height y if the winch M reels in cable at a constant rate ¡ . As- sume that the kayak remains level. -b b y M A b PROBLEM 2/186 B

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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