Simple Pendulum Problem: Finding Tension in the Connecting Rod

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Homework Help Overview

The discussion revolves around a simple pendulum problem involving the calculation of tension in the connecting rod at maximum angular displacement. The subject area includes concepts from mechanics, specifically forces acting on a pendulum.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive the tension using a free body diagram and geometric reasoning, leading to a different expression for tension compared to the textbook. Some participants question the validity of the original poster's reasoning and the assumptions made regarding the components of forces.

Discussion Status

The discussion has seen some clarification regarding the reasoning behind the tension calculation. One participant has provided an alternative perspective on the equilibrium of forces, suggesting that the equilibrium is along the direction of tension rather than perpendicular to it. This has led to a better understanding for the original poster.

Contextual Notes

There appears to be confusion stemming from differing approaches to resolving forces, particularly in how tension and gravitational components are treated. The original poster's method contrasts with the textbook's approach, highlighting a potential misunderstanding of the problem setup.

demonelite123
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A simple pendulum of length L and mass m swings about the vertical equilibrium position (θ=0) with a maximum angular displacement of θ_max. What is the tension in the connecting rod when th pendulum's angular displacement is θ=θ_max?

i drew a free body diagram and using simple geometry with triangles found that Tcosθ_max=mg so i solved and i got T = mg/cosθ_max. what i did was split the tension into components while leaving the gravity alone but the book did the opposite. they split the gravity into components while leaving the tension alone. so they got T=mgcosθ_max. i don't understand how my answer is incorrect.
 
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help please. is my reasoning correct? how come I'm not getting the same answer as my book?
 
No the reasoning is wrong. The equilibrium is along the direction of the tension and not perpendicular to it.The pendulum is momentarily at rest but still accelerated tangentially by gravity component gsin(theta).Hence T=mgcos(theta-max).
 
oh i understand now. that makes a lot of sense. thanks!
 

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