Drawing free body diagrams for pendulum

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SUMMARY

This discussion focuses on drawing and labeling the free body diagram of a pendulum at its maximum amplitude of 30 degrees. The correct representation includes the tension vector (T) directed diagonally upward and the gravitational force (mg) acting straight down, decomposed into components mgcos(30) and mgsin(30). It is established that at 30 degrees, the pendulum is momentarily at rest, meaning there is no centripetal acceleration at that point. The tension in the string is greater than the vertical component of the gravitational force.

PREREQUISITES
  • Understanding of free body diagrams
  • Knowledge of vector decomposition
  • Familiarity with pendulum motion and forces
  • Basic trigonometry, specifically sine and cosine functions
NEXT STEPS
  • Study the principles of static equilibrium in pendulum systems
  • Learn about the dynamics of pendulum motion at various angles
  • Explore the concept of centripetal force in oscillatory motion
  • Review vector analysis in physics, focusing on force diagrams
USEFUL FOR

Students in physics courses, particularly those studying mechanics, as well as educators looking to enhance their teaching of force diagrams and pendulum dynamics.

vu10758
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Homework Statement



I have to do this for a lab. Draw and label the free body diaggram of a pendulum when it is at its maximum amplitude of 30 degrees. The magnitudes of the vectors must be correctly scaled and the directions correct.


Homework Equations





The Attempt at a Solution



I drew the free body diagram with T pointing diagonally up and to the left. The arc angle is 30 degrees. I then draw gravity mg straight down with two components, mgcos(30) and mgsin(30). I reasoned that mgcos(30) is smaller than T in magnitude because the pendulum is in motion. The tension and centripetal force are in the same direction, and the pendulum is not at rest. Is my reasoning correct?
 
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Seems okay from your description, but we aren't going to know whether you fulfilled all the criteria for the free body diagram.

That first statement is confusing. An amplitude of 30 degrees?
 
Mindscrape said:
Seems okay from your description, but we aren't going to know whether you fulfilled all the criteria for the free body diagram.

That first statement is confusing. An amplitude of 30 degrees?


It means that at most the pendulum travels 30 degrees in either direction from equilibrium point.
 
vu10758 said:

Homework Statement



I have to do this for a lab. Draw and label the free body diaggram of a pendulum when it is at its maximum amplitude of 30 degrees. The magnitudes of the vectors must be correctly scaled and the directions correct.

Homework Equations



The Attempt at a Solution



I drew the free body diagram with T pointing diagonally up and to the left. The arc angle is 30 degrees. I then draw gravity mg straight down with two components, mgcos(30) and mgsin(30). I reasoned that mgcos(30) is smaller than T in magnitude because the pendulum is in motion. The tension and centripetal force are in the same direction, and the pendulum is not at rest. Is my reasoning correct?

At 30º the pendulum is momentarily at rest. There is no centripetal acceleration at that point.
 

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