Gravitational Field Strength Calculations with a Pendulum

Click For Summary

Discussion Overview

The discussion revolves around the calculations of gravitational field strength using a pendulum, specifically addressing the implications of pendulum length and motion type on the accuracy of the time period formula. The scope includes theoretical considerations and potential experimental implications.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the assumption of simple harmonic motion holds when the pendulum length is very small, suggesting that circular motion may affect the time period and consequently the value of g.
  • Another participant argues that if the goal is to find g, using a very small length that leads to circular motion introduces systematic error, emphasizing the importance of the assumptions in the period formula.
  • A participant seeks clarification on what is meant by a "plane" pendulum in the context of the discussion.
  • Another participant asserts that the pendulum's motion is always circular, regardless of amplitude, and explains that small amplitude assumptions allow for linearization of the motion equations.

Areas of Agreement / Disagreement

Participants express differing views on the effects of pendulum length and motion type on the accuracy of gravitational field strength calculations. There is no consensus on the implications of circular motion versus simple harmonic motion.

Contextual Notes

Participants highlight limitations in the assumptions underlying the time period formula, such as the need for small oscillation angles and the distinction between plane and conical pendulum motion, which remain unresolved.

matt_crouch
Messages
157
Reaction score
1
As a pendulum can be used to calculate the gravitational field strength by using the equation


Time period= 2(pi) sqrt (length/g)

this equation assumes that the pendulum bob is moving in Simple harmonic motion. However at very small lengths the pendulum bob tends to move in a more circular motion will this at all effect the time period and hense my value for g?

hopefully that makes sense =]
cheers
 
Physics news on Phys.org
It doesn't make sense, at least for me, because if you all you care about is to find "g", then why even make the length that small that it causes such circular motion?

And no, if you want it to be accurate, such circular motion can only add more systematic error to your estimation of g. Note that the formula for the period that you wrote assumes important simplifications: that the motion is a plane pendulum (not a 3D conical pendulum), and that it undergoes small oscillations, meaning a long pendulum with a small angle of oscillation. The more you deviate from that, the less accurate that period expression becomes.

Zz.
 
ahh thanks a lot... one thing how do you mean that the motion is a "plane" pendulum?
 
The motion of the pendulum is always circular, no matter whether it is small amplitude or large amplitude. It does not depend on the length of the pendulum.

The reason for assuming small amplitudes is so that the equation of motion can be linearized and reduced to a harmonic differential equation. For this to apply, only small amplitudes can be considered.
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 36 ·
2
Replies
36
Views
4K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 6 ·
Replies
6
Views
19K
  • · Replies 76 ·
3
Replies
76
Views
7K