P1.1.3.1 Determining the Gravitational Constant (Lightpointer)
Overview
Determining the gravitational constant with the gravitation torsion balance after Cavendish-measuring the excursion with a light pointer.
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Description
The heart of the gravitation torsion balance after Cavendish is a light-weight beam horizontally suspended from a thin torsion band and having a lead ball with the mass m 2 =15 g at each end. These balls are attracted by the two large lead spheres with the mass m 1 =1.5 kg.
F = G · m 1 ·m 2
r 2 r: distance between sphere midpoints
Although the attractive force is less than 10 -9 N, it can be detected using the extremely sensitive torsion balance. The motion of the small lead balls is observed and measured using a light pointer. Using the curve over time of the motion,the mass m 1 and the geometry of the arrangement, it is possible to determine the gravitational constant G using either the end-deflection method or the acceleration method.
In the end deflection method, a measurement error of less than 5 % can be achieved through careful experimenting. The gravitational force is calculated from the resting position of the elastically suspended small lead balls in the gravitational field of the large spheres and the righting moment of the torsion band. The righting moment is determined dynamically using the oscillation period of the torsion pendulum.
The acceleration method requires only about 1 minute of observation time. The acceleration of the small balls by the gravitational force of the large spheres is measured, and the position of the balls as a function of time is registered.
In this experiment, the light pointer is a laser beam which is reflected in the concave reflector of the torsion balance onto a scale. Its position on the scale is measured manually point by point as a function of time.
Cat. No. Description Quantity
332 101 Gravitation torsion balance 1
471 830 He-Ne laser 0.2/1 mW max., linearly polarized 1
313 05 Stopclock 1
311 77 Steel tape measure, 2m 1
300 02 Stand base, V-shape, 20 cm 1
301 03 Rotatable clamp 1
301 01 Leybold multiclamp 1
300 42 Stand rod, 47 cm 1
F = G · m 1 ·m 2
r 2 r: distance between sphere midpoints
Although the attractive force is less than 10 -9 N, it can be detected using the extremely sensitive torsion balance. The motion of the small lead balls is observed and measured using a light pointer. Using the curve over time of the motion,the mass m 1 and the geometry of the arrangement, it is possible to determine the gravitational constant G using either the end-deflection method or the acceleration method.
In the end deflection method, a measurement error of less than 5 % can be achieved through careful experimenting. The gravitational force is calculated from the resting position of the elastically suspended small lead balls in the gravitational field of the large spheres and the righting moment of the torsion band. The righting moment is determined dynamically using the oscillation period of the torsion pendulum.
The acceleration method requires only about 1 minute of observation time. The acceleration of the small balls by the gravitational force of the large spheres is measured, and the position of the balls as a function of time is registered.
In this experiment, the light pointer is a laser beam which is reflected in the concave reflector of the torsion balance onto a scale. Its position on the scale is measured manually point by point as a function of time.
Cat. No. Description Quantity
332 101 Gravitation torsion balance 1
471 830 He-Ne laser 0.2/1 mW max., linearly polarized 1
313 05 Stopclock 1
311 77 Steel tape measure, 2m 1
300 02 Stand base, V-shape, 20 cm 1
301 03 Rotatable clamp 1
301 01 Leybold multiclamp 1
300 42 Stand rod, 47 cm 1
; "P1.1.3.1 Determining the Gravitational Constant (Lightpointer)")