**Transcription of the Problem Statement from the Image:**A weight $ W $ is dropped from a height $ h $ on the mid-span at $ C $ of a simply-supported beam as shown, where the spring always remains vertical and is at its natural length when the beam is horizontal.For $ W = 90 \, \text{lb} $ and the stiffness of the spring $ k = 313 \, \text{lb/in} $, determine the static elongation of the spring ($ \delta_{\text{spring}} $) i.e., $ h = 0 $, [in].**Diagram Explanation:**1. **Beam Setup:** - A simply-supported beam $ AB $ is shown with supports at points $ A $ and $ B $. - The distance between $ A $ and $ B $ is noted as $ 40" $.2. **Weight Placement:** - A weight $ W $ is applied at the mid-span of the beam at point $ C $. - The weight is suspended from a height $ h $ directly above point $ C $.3. **Spring Details:** - There is a spring attached vertically at the end of the beam at point $ B $. - The spring has a stiffness constant denoted by $ k = 313 \, \text{lb/in} $.4. **Lengths and Measurements:** - The beam $ AB $ measures $ 40" $ from $ A $ to $ B $. - The length $ BC $ is $ 1" $. - An additional measurement from point $ B $ downwards is labeled $ 2" $.This scenario examines the static elongation of a spring when a weight is applied at the mid-span of a beam, considering the system reaches equilibrium without any initial height difference ($ h = 0 $).

Answered: when the beam is horizontal. For W-90…

when the beam is horizontal. For W-90 lb and the stiffness of the spring k-313 lb/in, determine the static elongation of the spring (6pring). Le, h-0. [in] W shown, wh

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

**Transcription of the Problem Statement from the Image:**

A weight $ W $ is dropped from a height $ h $ on the mid-span at $ C $ of a simply-supported beam as shown, where the spring always remains vertical and is at its natural length when the beam is horizontal.

For $ W = 90 \, \text{lb} $ and the stiffness of the spring $ k = 313 \, \text{lb/in} $, determine the static elongation of the spring ($ \delta_{\text{spring}} $) i.e., $ h = 0 $, [in].

**Diagram Explanation:**

1. **Beam Setup:**
- A simply-supported beam $ AB $ is shown with supports at points $ A $ and $ B $.
- The distance between $ A $ and $ B $ is noted as $ 40" $.

2. **Weight Placement:**
- A weight $ W $ is applied at the mid-span of the beam at point $ C $.
- The weight is suspended from a height $ h $ directly above point $ C $.

3. **Spring Details:**
- There is a spring attached vertically at the end of the beam at point $ B $.
- The spring has a stiffness constant denoted by $ k = 313 \, \text{lb/in} $.

4. **Lengths and Measurements:**
- The beam $ AB $ measures $ 40" $ from $ A $ to $ B $.
- The length $ BC $ is $ 1" $.
- An additional measurement from point $ B $ downwards is labeled $ 2" $.

This scenario examines the static elongation of a spring when a weight is applied at the mid-span of a beam, considering the system reaches equilibrium without any initial height difference ($ h = 0 $).

Expert Solution

Step 1: Write the given data with suitable variables-

$k equals 313 space lb divided by in W equals 90 space lb$

The free-body diagram is-

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