Measuring g, but not knowing the centre of mass - problem?

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Discussion Overview

The discussion revolves around measuring gravitational field strength (g) using a pendulum, specifically addressing concerns about the impact of not knowing the centre of mass of the pendulum on the experiment's results. Participants explore the implications of this uncertainty and potential solutions.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses confusion about the effect of not knowing the centre of mass on their experiment and seeks assistance.
  • Another participant asserts that not knowing the centre of mass will affect the results and suggests conducting a separate investigation to determine its location or making an educated guess.
  • It is mentioned that if the pendulum is a rigid mass rotating about a pivot, it is classified as a compound pendulum, which complicates the situation further due to the need for the moment of inertia.
  • A participant advises that designing the pendulum with a large length compared to the size of the bob is beneficial, although the specific advantages are not detailed.
  • One participant provides a formula for the period of a pendulum and discusses how the size of the bob can introduce uncertainty in the measurement of length and, consequently, in the period.

Areas of Agreement / Disagreement

Participants generally agree that not knowing the centre of mass will affect the experiment, but there is no consensus on the best approach to overcome this issue. Multiple viewpoints on how to address the uncertainty remain present.

Contextual Notes

The discussion highlights the dependence on the definitions of terms like "centre of mass" and "moment of inertia," as well as the potential for uncertainty in measurements based on the size of the bob relative to the length of the pendulum.

Who May Find This Useful

Students and educators involved in physics experiments related to gravitational measurements, pendulum dynamics, and those interested in the implications of experimental design on results.

sexysam_short
Hiya!

I'm confused, for my Physics A2 Coursework we're measuring g (gravitational field strength) and I don't know the centre of mass of the pendulum.

Will this affect my experiment and/or results? Should I do something to overcome it?

Please Help!

Sam(antha) xx
 
Physics news on Phys.org
Yes it will. You'll have to do a separate investigation to find the location of the centre of mass. Either that, or make an educated guess. Further, if the pendulum is a rigid mass that rotates about the pendulum pivot, it is actually a compound pendulum, and even the centre of mass won't tell you all you need. You'll need the moment of inertia. (But I can't imagine that the experiment is so poorly designed that you have to worry about these complications.)
You are best off if you can design your pendulum yourself. Then just make sure to make the length large compared with the size of the bob.
 
Thanks loads! What are the advantages of the length being large compared with the size of the bob?

So, will it be ok if I just basically measure the length of the string that the pendulum is made from?
 
Consider that the formula of the period is
[tex]T=2\pi\sqrt{l\over g}[/tex]
If the bob is an extended mass of unknown composition 1 cm in size and the string is 1m long, the length to the c.of.m is 1.005m plus or minus 5mm. So the length [itex]l[/itex] can be thought of as uncertain by the bob size, 0.5% in the case of the example I just gave. This makes the period uncertain by .25%. If the bob was 10cm in size, the period uncertainty would be 2.5%.
 
That makes loads of sense! Thank you lots again!
 

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