PASCO ME-9502 Statics System - Manual (Page 73)

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M o d e l N o . M E - 9 5 0 2 E x p . 1 1 C : S i m p l e H a r m o n i c M o t i o n – B e a m o n a S p r i n g
0 1 2 - 1 2 8 7 6 B 69
10. Measure and record the length of the beam, L, and the distance from the pivot point to the center of mass
(c.o.m.) of the beam, L
cm
.
11. See the experiment Hooke’s Law to find the spring constant, k, of the Spring Scale and record its value.
Calculations
1. Calculate and record the Measured Period for each trial.
2. Calculate and record the Average Measured Period for each lever arm length.
Assume that the Protractor is a point mass, m, at a distance r from the axis of rotation. Its moment of inertia added
to the beam’s moment of inertia gives the following:
Since the distance r from the axis of rotation is also the length of the lever arm, L
lever
, the moment of inertia
becomes:
and the period of oscillation, T, becomes:
3. Calculate the Theoretical Period, T
theoretical
, for each trial and record the result.
Data
• mass of beam, M = ____________ mass of protractor, m = ________________
• length, L = _____________ distance from pivot point to c.o.m., L
cm
= ________________
• spring constant, k = ________________
I I
beam
mr
2
+
1
12
------ML
2
ML
cm
2
mr
2
+ + = =
I I
beam
mr
2
+
1
12
------ML
2
ML
cm
2
mL
lever
2
+ + = =
T
2

L
lever
-------------- I
k
--
2

L
lever
--------------
1
12
------ML
2
ML
cm
2
mL
lever
2
+ +
k
---------------------------------------------------------------------- = =