PASCO ME-9341 INTRODUCTORY ROTATIONAL APPARATUS - Manual (Page 31)

012-03051F Introductory Rotational Apparatus
27
Exp 3 – Gravitational-Rotational Energy
Introduction
In this lab, results should verify conservation of energy to within 2% or better. Loss of energy will occur in the
bearings of the Rotational Apparatus, and in the pulley. This loss should remain relatively constant for various
masses pulling the thread. Therefore, for heavier falling masses, since the total energy exchange is greater, the
percentage error will be less. (This can be a useful point for student discussion.)
Alternatives
This experiment might be included in a laboratory in which different student groups carry out different experi-
ments, all related to energy conservation.
Notes – on Procedure
➂ Make sure that the thread is wound evenly—without overlapping itself—for best results.
➆ h
2
will change as the thread unwinds and stretches. Measure it in each trial for maximum accuracy.
smallest step used: r = 0.015
g = 9.8
h
1
= 0.651
Average Average Average
Mass (g) Force (N) h
2
ω
max max wt. vel. alpha
46.35 0.4542 0.0880 8.1307 0.1220 0.8883
96.74 0.9481 0.0840 11.9843 0.1798 1.8756
147.01 1.4407 0.0810 14.7693 0.2215 2.8722
197.22 1.9328 0.0790 17.3205 0.2598 3.9055
Notes – on Analysis
I = 7.75E-3
mgh 1/2 I
ω
2 1/2 m v 2 RKE + KE % error (1) % error (2)
0.2557 0.2562 0.0003 0.2565 0.17% 0.31%
0.5375 0.5565 0.0016 0.5581 3.53% 3.82%
0.8212 0.8453 0.0036 0.8489 2.93% 3.37%
1.1055 1.1625 0.0067 1.1692 5.15% 5.75%
Note that in each case the final energy of the system (RKE+ KE) is greater than the original energy (mgh). This is
rather unsettling... (not to mention wrong!) As near as I can tell, the actual moment of inertia of the platter is less
than the value listed in the manual. You can experimentally check the moment of inertia of your own platter (they
vary some due to manufacturing differences) by assuming conservation of energy and then solving for I:
mgh = 1/2 I
ω 2
+ 1/2 m v
2
where w is the angular velocity and v is the linear velocity of the mass m.Using this method, I found the moment
of inertia to be 7.50x10
-3
± 3%. This value for I gives me much better results, although the energy is still too high.