To accommodate the rise and fall of the tide, a walkway from a pier to a float is supported by two rollers as shown. If the center of mass of the 590-lb walkway is at G, calculate the tension $ T $ in the horizontal cable which is attached to the cleat and find the magnitude of the force under the roller at A.### Diagram Description:- The image shows a side view of a pier and a floating structure on water.- A walkway spans from the pier to the floating structure, angled downward at $ 25^\circ $ from the horizontal.- The total length of the walkway is $ 20' $.- The center of mass, labeled $ G $, is located $ 10' $ from the roller at $ A $ and $ 10' $ from the roller at $ B $.- A horizontal tension $ T $ acts at the top right of the walkway.- The roller at point $ A $ is on the lower left, situated on the pier.- A force acts upward at the roller at $ A $.This setup requires calculating the equilibrium conditions considering the forces at play, including gravitational forces, tension in the cable, and normal forces at the rollers.

Answered: the center of mass To accomodate the…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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To accommodate the rise and fall of the tide, a walkway from a pier to a float is supported by two rollers as shown. If the center of mass of the 590-lb walkway is at G, calculate the tension $ T $ in the horizontal cable which is attached to the cleat and find the magnitude of the force under the roller at A.

### Diagram Description:
- The image shows a side view of a pier and a floating structure on water.
- A walkway spans from the pier to the floating structure, angled downward at $ 25^\circ $ from the horizontal.
- The total length of the walkway is $ 20' $.
- The center of mass, labeled $ G $, is located $ 10' $ from the roller at $ A $ and $ 10' $ from the roller at $ B $.
- A horizontal tension $ T $ acts at the top right of the walkway.
- The roller at point $ A $ is on the lower left, situated on the pier.
- A force acts upward at the roller at $ A $.

This setup requires calculating the equilibrium conditions considering the forces at play, including gravitational forces, tension in the cable, and normal forces at the rollers.

Expert Solution

Step 1

Centre of mass

The centre of mass is a location determined in respect to an object or group of things. It represents the average location of the system, weighted by the mass of each component. The centre of mass of an object or system is interesting because it determines where any uniform force acting on the object will act.

centre of mass (G)= 590 lb

The walkway is placed at an angle of $25 °$

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