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Brand: AELAB
Determining the gravitational acceleration with a reversible pendulum
 Reversible Pendulum: Length L = 120cm, Distance between 2 edges d = 80cm. There are 25 lines in Stainless steel rod, 2.5cm apart. There are 2 weights with m1 = 940g and m2 = 1360g. Edge holder is wall attachable.
 Ruller 30cm
 Measuring the oscillation periods T1 and T2 of a reversible pendulum for two suspension points.
 Tuning the reversible pendulum to the same oscillation period.
 Determining the gravitational acceleration from the oscillation period and the reduced length of pendulum.
With compound pendulum, the oscillation formula:
(1)
J: Moment of inertia of pendulum via oscillation axis (H1 or H2).
s: Distance from weight (m2) to oscillation axis (H1 or H2).
g: Gravitational acceleration.
m: Mass of pendulum.
The reduced length Sr of the compound pendulum is defined as the quantity:
(2)
because its oscillation period:
(3)
corresponds to that of a simple pendulum with the length Sr.
The moment of inertia J of the compound pendulum is, according to the parallel axis theorem:
(4)
Js: moment of inertia around the centre of mass axis.
Therefore the reduced length of pendulum is:
(5)
The reversible pendulum is a particular type of the compound pendulum. There are two edges H1 and H2 that allow to choose the suspension point.. Two weights m1 = 940g và m2 = 1360g can be shifted so that the oscillation period is tunable. The goal of the tuning is to achieve equal oscillation periods around both edges
When T1 = T2, In this case, the reduced length of pendulum is equal:
(6)
s1 and s2 is distance from weight m2 to H1 anf H2. Then:
(7)
d: distance from H1 to H2.
From formula (6) and (7):
(8)
S1 is inserted in Eq (5):
(9)
Then:
(10)
Set up and procedure:
Reversible Pendulum (Kater's pendulum)
 Mount the wall holder on a stable, nonvibrating wall.
 Attach photogate to wall (by screw), so that pendulum scan to IR eye of photogate (see the clip below)
 Fix the mass m1 at the position x1 = 10 cm from H1 (position of m1 can be changed)
 We do experiment with m2 at position x2 = 9.7; 12.2; 14.7 cm; .... 69.7cm from H1 (the top line of pendulum is away from axis of oscillation H1 9.7cm)
Measure period by 2 ways:
+ The first way: Select Mode 4 in photogate timer. To measure period in directly.
+ Second way: Select Mode 5 in photogate timer: Count 50 periods, measure total time. Then calculate average period.
We recommend the second way for better accuracy.
 Deflect the pendulum a small angle, the rod of reversible pendulum cover IR eye of photogate. Release the rod, the Kater's pendulum will oscillate.
 Press Start/Stop button to count. Wait for counting 50 periods then press Start/Stop again to stop count.
 Write the total time for 50 periods to data table.
 Slide the weight m2 to second line position (x2 = 12.2cm). Measure 50 periods again.
 After we do with the 25th line (x2 = 69.7cm). We reverse the pendulum, the axis of oscillation is H2.
Reversible Pendulum: Axis H2
 We do experiment again similar to doing with axis H1.
 We have the experiment data below:
Use this formula to determine the gravitational acceleration:
(10)
The graphs T1 and T2 intersect at: 3.154 and 3.334
From formula (10) above, so g1 = 10m/s2, g2 = 9.46m/s2
Average value: g = 9.73m/s2
Error: 0.82%