Скачать или смотреть Home-built Cavendish gravity experiment -- accurate measurement of gravitational force

Gravity is by far the weakest of the fundamental forces of nature. It takes a very sensitive instrument isolated from vibration and stray forces to measure the gravitational force accurately and without artefacts. In this experiment, a torsional pendulum (arm length 7.5 cm) is suspended by a thin tungsten wire (58 micrometers diameter, 80 cm long). The pendulum is formed from two 20 mm copper cubes soldered to a 20 mm x 170 mm x 1.2 mm copper plate. The tungsten wire is connected to a guitar tuning mechanism which allows precise adjustment of the height and also provides rotational freedom. The pendulum is supported by a thick wooden plank attached to a heavy bookshelf, which in turn is secured to a brick wall.

The pendulum is housed in a balsa-wood box that is lined with thin copper foil (0.01 mm thick). Copper sheet (0.1 mm thick) is placed on the outside, forming a thermal loop between the front and back of the box. A foam-board box then surrounds this structure to provide thermal insulation. Finally, a thicker layer of copper sheet (0.2 mm) shields the outside and provides another thermal loop. The main purpose of the copper foil and sheets is to prevent a temperature differential from causing a disturbing force. Small temperature differences will cause air expansion or contraction that will displace the pendulum. The main issue is a temperature difference between the lead balls and the copper cubes.

2.2 kg lead balls serve as the attracting masses and are positioned 9.2 cm from the copper cubes. A laser beam reflects off a mirror mounted on the pendulum and is focused on a paper screen 61 cm from the axis of the pendulum. The motion of this spot indicates the angle through which the pendulum deflects under the influence of gravitational attraction. The time period of the pendulum is 8.0 min (480 seconds).

Photos of the moving laser spot were taken every 10 sec and analysed in real time. The magnitude of the oscillation (motion in x) and vertical noise (motion in y) were calculated using two red spots (spaced 1.00 inch apart) printed on the paper screen as reference markers. When the lead balls are moved, the lowest energy position of the pendulum shifts due to the change in gravitational field. The equilibrium position can be calculated by taking the average of the peaks in the oscillation [(x1+x3)/2+x2]/2. As seen in the chart in the film, the difference in the equilibrium positions (an indication of the change in gravitational potential) is found to be slightly less than 3 mm, in agreement with theory to within 3%.

Our calculated equilibrium displacement is 2.8 mm. The precise theoretical value of the displacement depends upon calculating the moment of inertia of the pendulum, the geometric anti-torque of the distant cube and the attraction and anti-torque of the pendulum beam. These calculations are rather complex and in total give a correction factor of 1.19 versus a simple ideal torsion pendulum. In terms of gravitational field, the copper cubes can be treated as spheres (and therefore as point masses) for distances greater than several edge lengths. The main correction factor (1.16) is the anti-torque of the distant cube (the contributions of the beam -- additional moment of inertia and additional gravitational attraction -- almost cancel).