Simple Pendulum Problem: Finding Tension in the Connecting Rod

In summary, the tension in the connecting rod of a simple pendulum with a maximum angular displacement of θ_max is equal to mgcosθ_max. This is determined by considering the equilibrium along the direction of the tension, rather than perpendicular to it. The pendulum is also accelerated tangentially by the gravity component gsin(theta).
  • #1
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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  • #2
help please. is my reasoning correct? how come I'm not getting the same answer as my book?
 
  • #3
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).
 
  • #4
oh i understand now. that makes a lot of sense. thanks!
 

1. What is a simple pendulum?

A simple pendulum is a weight suspended from a pivot point that is free to swing back and forth under the influence of gravity.

2. How is the period of a simple pendulum calculated?

The period of a simple pendulum is calculated using the equation T=2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

3. What factors affect the period of a simple pendulum?

The period of a simple pendulum is affected by its length, the mass of the weight, and the strength of gravity.

4. How does the angle of release affect the period of a simple pendulum?

The angle of release does not affect the period of a simple pendulum as long as the amplitude (maximum angle of swing) is small (less than 15 degrees).

5. Can the period of a simple pendulum be affected by air resistance?

Yes, air resistance can affect the period of a simple pendulum by slowing down its motion, but this effect is usually negligible for small amplitudes.

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