### Educational Text on Mechanical System Analysis:#### Consider the System in Figure 1**Problem Statement:**Determine the smallest amount the spring at point \( B \) must be compressed against the 0.7-lb block so that when the block is released from \( B \), it slides along the smooth surface and reaches point \( A \). **Instructions:**- Express your answer in inches to three significant figures.**Input Required:**- Enter the value of \( x = \) ______ in.**Interface Elements:**- Calculation tools are available, including vector analysis and various mathematical functions.**User Actions:**- Submit your answer through the provided input box.- If needed, you can request an answer for assistance.**Feedback Option:**- Provide Feedback link is available for user interaction.---#### Detailed Explanation of the Diagram in Figure 1:- The diagram depicts a mechanical spring system.- **Spring Details:** - The spring constant \( k \) is given as 5 lb/in.- **Block Details:** - A 0.7-lb block is positioned against the spring at point \( B \).- **Pathway Description:** - The block is intended to slide from point \( B \) to point \( A \) along a smooth surface. - Path follows the equation \( y = \frac{1}{2} x^2 \).- **Dimensions:** - The horizontal distance from position \( B \) to point \( A \) is 1 ft.This setup investigates the principles of energy conservation and mechanical motion, specifically focusing on potential and kinetic energy transformations within the system.

Answered: Image /qna-images/answer/757d8e66-c915-4482-8999-13947f2dbd71.jpg

Answered: Consider the system in (Figure 1).…

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