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16
acceleration (
x = 1/2 at
2
), the acceleration can be calculated:
a
0
= 2
Δ
s/t
2
=
Δ
Sd/t
2
L
(3.6)
By monitoring the motion of the light spot over time, the
acceleration can be determined using equation 3.6, and the
gravitational constant can then be determined using equation
3.4.
Procedure
1.
Begin the experiment by completing steps 1–3 of the
procedure detailed in Method I.
2.
Immediately after rotating the swivel support, observe the
light spot. Record the position of the light spot (
S
) and the
time (
t
) every 15 seconds for about two minutes.
Analysis
1.
Construct a graph of light spot displacement
(
Δ
S = S - S
1
) versus time squared (
t
2
), with
t
2
on the
horizontal axis (Figure 20). Draw a best-fit line through
the observed data points over the first minute of
observation.
2.
Determine the slope of your best-fit line.
3.
Use equations 3.4 and 3.6 to determine the gravitational
constant.
4.
The value calculated in step 3 is subject to a systematic
error. The small sphere is attracted not only to its
neighboring large sphere, but also to the more distant
large sphere, although with a much smaller force. Use the
procedure detailed in Method I (
Analysis, step 3
) to
correct for this force.
Δ
S
t
2
(sec
2
)
0
1
2
3
4
5
6
7
8
9
225 2025
900
3600
5625
8100
11025
BEST FIT LINE
CURVE
THROUGH
DATA
Figure 20
Sample data and best-fit line
Summary of Contents for AP-8215
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