Simple Pendulum Problem: Finding Tension in the Connecting Rod

[demonelite123]

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.

 

[demonelite123]

help please. is my reasoning correct? how come I'm not getting the same answer as my book?

 

[aim1732]

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).

 

[demonelite123]

oh i understand now. that makes a lot of sense. thanks!