June 25, 2006                          College Physics                        Chance Moore             1/1

                                             Extra Credit Project

Problem:  What is the period and moment of inertia of a heavy bag that is set into SHM by a left hook?

Given:  The bag has a mass of 26.4 kg.

            The length of pendulum is 129.5 cm.

            Gravity  =  9.8 m/s²

            It will act like a physical pendulum.

Assumptions:   Since the first 27.9 cm are chain, the center of gravity will be lower than 50% of the length, so it will be assumed it is 40% of the length from the bottom.

Equations:   I  =  ⅓ ml²

                    T =  2 π √_ I __ ≈  2 π √  _I__

                                     T/0                  mgh

Theory:  Using the given information and experimental data, the moment of inertia will be found.  Also, using the equations, the period should be near the experimental measure of period. 

Experimental data:  T (Experimental) =  2.06s               4 periods in 8.25s

Calculations:  I  =  ⅓ • 26.4 • 1.295² = 14.8n

                       T(Calculated) = 2 π √____14.8_______     = 2.95

                       Calculated                   26.4 • 9.8 • 0.518²         

                       40% • 1.295 = 0.518

Results:  I = 14.8n                                            error = 29%

  T (experimental) = 2.06s

  T (calculated) = 2.95