The Law of Conservation of Energy says that an object with a specific potential energy, when falling will convert that energy to kinetic energy. The purpose of this lab was to prove that this occurs. The apparatus used consisted of a rotating vertical shaft, and a centered horizontal crossbar atop the vertical shaft with wingnuts and masses. A mass hanger was attached to the string and ran over a seemingly frictionless pulley system. When the hanger was dropped, the shaft rotated, causing the horizontal cross bar to go into rotation about the vertical shaft. The linear kinetic energy from the falling masses on the hanger was converted to rotational energy of the horizontal crossbar. .
The moment of Inertia of this system should theoretically be I=2MR2 where M is equal to the weight added to one side of the crossbar, I is equal to the inertia, and R is the distance between the vertical shaft and the masses. The theory was tested through treating the radius of the crossbar and the amount of mass as independent variables. .
The first set of measurements was taken using two 100g slotted masses on the horizontal cross bar. The distance between the center of the vertical crossbar (r) and the masses was measured to be .102m the distance that the hanger of 50g was to fall (h) was measured as 88.1cm. The string was then wrapped tightly about the upright and moved to .881m above the ground As the hanger was let go, a stopwatch was simultaneously started. When the hanger's fall was finished, the stopwatch was stopped. The procedure was repeated twice and the times were averaged. Times were then recorded with the 100g masses removed, but the wingnuts in the same spots. .
To establish a relationship between the weights and the measured inertia of their mass, measurements were taken using 150g to 350g masses, however, the r of 10.2cm was constant. The results are posted in the data table listed below.
Data Table of Mass and Times:.
