Calculating Gravity with Pendulum - Factors of influence

Click For Summary
SUMMARY

This discussion focuses on calculating gravity using a pendulum, specifically addressing the formula T = 2π√(L/g) and the factors influencing the results. The participant achieved an average gravity measurement of 9.53 m/s², which deviates from the expected 9.8 m/s² due to factors such as human reaction time, friction, air resistance, and weight distribution. Additional considerations include the gravitational interaction between the pendulum mass and its support, the elasticity of the string, and the impact of large angle swings on the accuracy of the simple harmonic motion assumption.

PREREQUISITES
  • Understanding of pendulum mechanics and simple harmonic motion
  • Familiarity with the formula T = 2π√(L/g)
  • Knowledge of factors affecting pendulum motion, including air resistance and friction
  • Basic principles of experimental measurement and uncertainty
NEXT STEPS
  • Research the effects of air resistance on pendulum motion
  • Learn about measuring pendulum periods accurately, including timing techniques
  • Explore the impact of string elasticity on pendulum length and motion
  • Investigate the conditions under which simple harmonic motion applies to pendulums
USEFUL FOR

Students conducting physics experiments, educators teaching pendulum mechanics, and anyone interested in the precise measurement of gravitational acceleration.

MassivePhysics
Messages
2
Reaction score
0
Sorry if I fill any of this out incorrectly, this is my first post.

Homework Statement


Basically, we are told to calculate gravity with the use of a pendulum. Now, this part I understand, alter the length, record the period at each length, calculate averages and substitute these averages into the formula, T = 2pi sqrt (L/g)


Homework Equations


As stated above.


The Attempt at a Solution


I have obtained my average for gravity, which is 9.53m/s^2. But I need some clarification on a few minor things.

In my scientific discussion, I have said that:
-human reaction time
-Friction
-Air resistance
-Weight Distribution (of the mass on the end of the pendulum)

All play a part in the result for gravity not being 9.8, however there are a few things that I am tempted to include, but not too sure if they are correct.

1. The very, very, very small impact that the gravitation force between the metal mass on the end of the pendulum and the metal retort stand used to hold the pendulum has. I.e, this small gravitation field is slightly altering the course of the pendulum and as such slightly altering the period time.

2. The elasticity of the string (fishing line) used on the pendulum. Wouldn't there be a very small amount of elasticity which would be altering the length of the string throughout the course of its period?

Any help would be really appreciated.
 
Physics news on Phys.org
Remember the formula you mentioned to find out time period is only applicable for Pendulum performing Simple Harmonic Motion, that is, by undergoing (infinitesimally) small displacement. So, for Macro-displacements, the motion is no longer SHM and the formula is not very accurate.
 
I would assume that the reason free fall acceleration is so deviated is that the experiment was performed using large angles of swinging, up to about 15 degrees should have been good enough.

You could include that the length of the pendulum may not have been measured precisely, also the uncertainty in your timekeeping device.

Also, the larger angle you use the faster speed pendulum bob obtains, since the force of air resistance is proportional to the square of the speed, that influenced the period slightly.
 
MassivePhysics said:
1. The very, very, very small impact that the gravitation force between the metal mass on the end of the pendulum and the metal retort stand used to hold the pendulum has. I.e, this small gravitation field is slightly altering the course of the pendulum and as such slightly altering the period time.
Much too small to be of interest.
 
How did you measure period? Did you time one swing, or time ten swings and divide by ten? If you used multiple swings, mis-counting happens sometimes.
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
Replies
3
Views
2K
  • · Replies 27 ·
Replies
27
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 31 ·
2
Replies
31
Views
4K