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C
AVENDISH
Cavendish Gravitational Balance KSCICGB
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DESCRIPTION OF THE INSTRUMENT
The CGB001 Cavendish Gravitational Balance is a miniature version of the apparatus
used by Henry Cavendish in 1797-8 to measure the density of the Earth. The experiment
allows the value of the gravitational constant, G, to be measured, although Cavendish
did not use his version for that purpose. The experiment is remarkable for the ability to
measure an extremely tiny force using simple mechanical means.
The apparatus contains a pendulum system (1, Figure 1) consisting of an adjustable
suspended central rod carrying a small mirror for the optical lever detection system, a
light aluminum cross-piece with two 20g lead balls 10 cm apart, and a light damping
vane. The pendulum is mounted in a massive aluminum housing (2). Two large 1.5 kg
plastic-coated lead balls (4) rest atop light aluminum cylinders on a swivel (4) that enables
the balls to be swung from one side to the other of the apparatus. They can also be
placed onto two circular sliding mounts (6) that allow the distance between the pendulum
and the attracting masses to be varied. The base rests on three leveling feet (6).
An oil reservoir and damping oil (7) as well as a damping magnet (8) are provided.
847-336-7556
www.unitedsci.com
G
RAVITATIONAL
CGB001
Figure 1
www.KlingerScientific.com
B
ALANCE
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Summary of Contents for KLINGER KSCICGB
- Page 1 AVENDISH RAVITATIONAL ALANCE Cavendish Gravitational Balance KSCICGB CGB001 Figure 1 DESCRIPTION OF THE INSTRUMENT The CGB001 Cavendish Gravitational Balance is a miniature version of the apparatus used by Henry Cavendish in 1797-8 to measure the density of the Earth. The experiment allows the value of the gravitational constant, G, to be measured, although Cavendish did not use his version for that purpose.
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Page 2: Specifications
SPECIFICATIONS Figure 1 IDENTIFICATION OF THE COMPONENTS Upper suspension rod locknut Aluminum body Pendulum angle adjustment block Swinging support for large lead balls Suspension rod height adjusting nut Scale (on base—1 of 2) Angle indicator disk Base plate Angle scale disk Leveling nut (1 of 3) Suspension rod locking screw (1 of 2) Foot (1 of 3) - Page 3 The torsion balance is housed in a solid aluminum main body (18) with glass win- dows (9) on both sides to eliminate drafts. The adjusting nut (3) on the top can be used to raise or lower the upper suspension rod (7) in order to adjust the vertical position of the balance.
- Page 4 THEORY The most common methods used to measure the value of the gravitational constant are the displacement method and the acceleration method. The Displacement Method Figure 2 Figure 3 The displacement method is named after the final angular displacement of the torsion balance to be measured in the experiment.
- Page 5 the dotted line and small circles in Figure 2. Its angle of rotation to the new equilibrium position can be determined by the displacement (=2s) of the projected dot on the scale. The distance from the mirror to the screen being , and S «...
- Page 6 Figure 4 There is a second, more important correction, illustrated by Figure 4. The small ball is subjected not only to the force applied by the large ball , but also to a force applied by the large ball . Therefore, the value for obtained from expression (6) needs to be corrected.
- Page 7 The force actually acting on the small ball is Substituting this into expression (4), we have Since the corrected expression for ...
- Page 8 we can apply Newton’s Law F where is the acceleration. Substituting into (10), we have (11) Expression (11) can be corrected to take into account the gravitational force applied by the second large ball: (12) ...
- Page 9 F therefore So the relationship between F and r will be verified if we can show experimentally that S Figure 6 Figure 6 illustrates the change in the distance between the large and small balls. Record the displacement of the light dot and the corresponding distance then plot on graph paper to verify that the relationship between...
- Page 10 Use the leveling screws (22) to adjust the angle of the apparatus so that the lower suspension rod (34) hangs in the center of the hole in the balance centering plate (11). Apply torsion to the filament using the angle adjustment block (2) until the small balls just touch the glass window, then finely adjust the leveling screws for the largest displacement of the light dot on the screen.
- Page 11 x’ = x , the balance is in its equilibrium position. If not, adjust the angle adjustment x = x’ block (2) and repeat the measurement until EXPERIMENTS A The Displacement Method 1. Measurement of the period of the torsion balance With the balance swinging with a moderate amplitude and not touching the glass ...
- Page 12 Example: In an experiment using air damping, the experimenter measured the following quantities: Mass of each large lead ball, 1.520 kg 2.124 m Projection distance, Period of the torsion balance, 596.3 sec. Distance between the large and small balls, 4.75x10 Length of the balance arm, 5x10 When the large balls were at their initial positions, three consecutive end points of...
- Page 13 B The Acceleration Method Do not use the damping oil for this method. Drain the oil from the main body by lowering the oil cylinder – the oil will flow back into the cylinder. Place the large balls in their initial positions as shown by the solid lines in ...
- Page 14 The slope, , is given by = (4x485.0-19350x0.0855)/(4x1.143x10 -3.744x10 = 3.44x10 Therefore, Solving for and substituting into expression (11), = ((4.75x10 x7.578x10 )/(2x1.5 = 5.624x10...
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Page 15: Maintenance
values are shown in Table 3. A graph of (1+b)S vs. r can be plotted with the data in Table 3. See Figure 9. The graph verifies the linear relationship: Figure 9 MAINTENANCE Lock up the torsion balance with the locking knob after each experiment. ... -
Page 16: Important Note
the cause could be air convection due to temperature change, oil flowing into or out of the damping trough, a build-up of electrostatic charge, or external vibration nearby (air conditioner, compressor, refrigerator, footsteps, etc.) To obtain optimal performance, conditions should be kept as calm as possible. Avoid touching the apparatus or the bench, moving chairs around, etc., as much as possible. - Page 17 Using the pendulum locking mechanism screw on the left side of the instrument, carefully raise the pendulum until it is secured against the body of the case at the top of the pendulum cutout. Be careful not to over-tighten the mechanism, as this can bend the pendulum arm.
- Page 18 on the end of the pendulum stem or the head of the set screw. DO NOT ALLOW THE WIRE TO KINK AT THE LUG SOLDER POINT! If the pendulum is not already angled, loosen the pendulum arresting mechanism slightly and turn the pendulum about 45°. Gently grasp the free lug with the tweezers, raise it a little so that the slot matches the set screw head position, and gently slide the lug into place under the head of the set screw.
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