Lab report just calculation parts only

The Simple Pendulum –Lab

Purpose

The objective of the lab is to test the dependence of length and starting angle on the period of a simple pendulum.

Material

String of approximate length 100-150cm, mass to attach to one end of the string, ruler, stopwatch, protractor, tape, or other fasteners to anchor the string.

Background

The period of a simple pendulum, T, is given by T = 2π*(ℓ/g)1/2

Experimental Procedure

Attach a mass such as a tennis ball (or a plumb bob, which you can buy for around 10 dollars at Home Depot, Ace Hardware, or similar) to the end of a string.  One option for this assembly would be to wrap the string a few times around the ball and then taping up the end of the string.  If you can come up with another method, that’s fine, just include what you did in your report.  If you use a tennis ball in your setup, it will have a circumference of 21 cm, and you will need to account for this in the length of string you use.

Anchor the pendulum assembly to a thin, horizontally-aligned edge.  Do your best to make sure that the string rubs against the anchor point as little as you can make it.  The length of the pendulum will be the length of the string from the pivot point to the top of the hanging mass plus the radius (or half the height if your mass isn’t round) of your mass.  You’re looking for something around 30 cm for the pendulum length. Once you have your experimental assembly in place, you will do a total of six measurements.  At the first pendulum length, run trials with a starting angle of 15, 30, and 45 degrees from vertical.  Repeat this for a shorter length, which you can get by either wrapping the anchor end of the pendulum around whatever anchor you use or by simply cutting the string. Take a measurement for ten periods of the pendulum in each of the six experimental configurations given above and then divide by ten to get your experimental value of the pendulum’s period for each trial.

Analysis and Discussion

The focus of the analysis will be somewhat different for this lab.  Your period measurement should be pretty precise, down to approximately millisecond timing.  Your predicted period, however, will carry some uncertainty because of the uncertainty of determining the precise length of the pendulum.  You should make an estimate of the uncertainty in length and give a brief justification for this estimate.

Once you have made the estimate of the error in the length of the pendulum, you can figure out the range of predicted values for a period as follows. Since the period depends on the 1/2 -power of length, the fractional error in the predicted value of T goes as:

                     (δT)/T = (δℓ)/2ℓ

Where δℓis the uncertainty in the length of the pendulum bob that you estimated earlier.  This means you will have a range of T ± δT for your predicted value of T, which you will then measure as described in the Experimental Procedure section.  Does your measured fall within the range of predicted T ± δT?  If not, discuss why this may have happened, and what you might do to improve the experiment.