8-45. The beam AB has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass of 50 kg and negligible thickness. Determine the minimum force P needed to move the post. The coefficients of static friction at B and C are µg = 0.4 and #c= 0.2, respectively.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem 8–45:**

The beam \( AB \) has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass of 50 kg and negligible thickness. Determine the minimum force \( P \) needed to move the post. The coefficients of static friction at \( B \) and \( C \) are \( \mu_B = 0.4 \) and \( \mu_C = 0.2 \), respectively.

**Diagram Explanation:**

- The diagram illustrates a beam \( AB \) with a triangular distributed load gradually increasing to 800 N/m at point \( B \).
- Point \( A \) is a fixed pin support, allowing rotation but preventing translation.
- At point \( B \), the beam extends 2 meters horizontally from point \( A \).
- A vertical column at point \( B \) is 400 mm (0.4 meters) high, resting on a post \( C \), which is 300 mm (0.3 meters) tall.
- The post \( C \) is connected to a force \( P \) applied at the top of the post, with an inclination described by a \( 3-4-5 \) triangle.
- The coefficients of static friction are specified for points \( B \) and \( C \).

This setup implies a calculation for the minimum force \( P \) to overcome static friction and move the post supporting the beam under the given loading.
Transcribed Image Text:**Problem 8–45:** The beam \( AB \) has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass of 50 kg and negligible thickness. Determine the minimum force \( P \) needed to move the post. The coefficients of static friction at \( B \) and \( C \) are \( \mu_B = 0.4 \) and \( \mu_C = 0.2 \), respectively. **Diagram Explanation:** - The diagram illustrates a beam \( AB \) with a triangular distributed load gradually increasing to 800 N/m at point \( B \). - Point \( A \) is a fixed pin support, allowing rotation but preventing translation. - At point \( B \), the beam extends 2 meters horizontally from point \( A \). - A vertical column at point \( B \) is 400 mm (0.4 meters) high, resting on a post \( C \), which is 300 mm (0.3 meters) tall. - The post \( C \) is connected to a force \( P \) applied at the top of the post, with an inclination described by a \( 3-4-5 \) triangle. - The coefficients of static friction are specified for points \( B \) and \( C \). This setup implies a calculation for the minimum force \( P \) to overcome static friction and move the post supporting the beam under the given loading.
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