A 30-cm diameter solid steel sphere hangs from cables as shown. Find the tension in cables AB and AC. For the density of steel, use p= 7270 kg/m^3 The image shows a diagram of a pendulum system. It consists of a spherical bob labeled as point A, which is suspended by two cords. These cords are attached to points B and C on a horizontal support.- The angle between the cord from point B to point A and the vertical is labeled as 45 degrees.- Similarly, the angle between the cord from point C to point A and the vertical is also labeled as 45 degrees.This setup forms two right-angled triangles, each with one side along the vertical axis and one sloping at a 45-degree angle. The symmetry of the angles implies that the tensions in the cords may be equal, depending on the mass of the bob and other forces acting on it. This type of system is often used to study equilibrium and tension forces in physics.

Given:- The diameter of the solid steel sphere = 30 cm The density of the steel used = p= 7270 kg/m3 To determine:- The tension in cables AB and ACA free-body diagram of the system Here, W = Weight of the solid steel ball T = Tension developed in each cable The weight of the solid steel ball hung can be calculated using the formula W=m×g Here, m = Mass of the steel ball g = Acceleration due to gravity = 9.81 m/s2 The mass of the steel ball will be m = p×V Here, p = Density of the ball = 7270 kg/m3 V = Volume of the solid ball V = 43×π×r3 r = radius of the ball = d2 d = diameter of the ball = 30 cm = 0.3 m r = 0.3 2m So, The weight of the solid steel ball hung will be W=7270×43×π×0.323×9.81W=7270×43×π×3.375×10-3×9.81W=7270×0.01413×9.81W=102.777×9.81W=1008.244 NNow, The tension in cables AB and AC will be Considering the tension developed in both the cable will be similar due to symmetry Applying equilibrium equations ∑FY=0T×cos 45°+T×cos 45°=W Putting, W = 1008.244 N 2×T×cos 45°=1008.244T=1008.2442×cos 45°T=1008.2441.4142T=712.936 N Hence, The tension in cables AB and AC = T = 712.936 N

Answered: A 30-cm diameter solid steel sphere…

Engineering

Civil Engineering

A 30-cm diameter solid steel sphere hangs from cables as shown. Find the tension in cables AB and AC. For the density of steel, use p= 7270 kg/m^3

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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A 30-cm diameter solid steel sphere hangs from cables as shown. Find the tension in cables AB and AC. For the density of steel, use p= 7270 kg/m^3

The image shows a diagram of a pendulum system. It consists of a spherical bob labeled as point A, which is suspended by two cords. These cords are attached to points B and C on a horizontal support.

- The angle between the cord from point B to point A and the vertical is labeled as 45 degrees.
- Similarly, the angle between the cord from point C to point A and the vertical is also labeled as 45 degrees.

This setup forms two right-angled triangles, each with one side along the vertical axis and one sloping at a 45-degree angle. The symmetry of the angles implies that the tensions in the cords may be equal, depending on the mass of the bob and other forces acting on it. This type of system is often used to study equilibrium and tension forces in physics.

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