GRAVITATION

Film Loop: Measurement of 'G': the Cavendish experiment

Length: 4:25 min., Black and White, No sound

Newton's law of universal gravitation is F=Gm1m2/(r squared) where F is the force between two point masses m1 and m2 which are separated by a distance r. The object of the experiment is to determine G. Small lead balls, each of mass m, are supported on a T-shaped frame which is suspended by a fine wire to form a torsion pendulum. Large lead spheres each of mass M are placed as shown, exerting a torque on the moving system. The system is allowed to come to rest, and the equilibrium position is shown by a light beam reflected to a scale.

The large lead balls are then shifted to give an equal and oppositely directed torque, and the system comes to a new equilibrium position. The approach to equilibrium is a damped SHM and requires over 1 1/2 hours. The motion of the scale indicator is shown in time lapse in the final segment of the film. The final measured position is just under 58.0 cm, and the deflection is 57.95 cm- 51.8 cm = 6.15 cm on a scale 154 cm from the mirror of the moving system.

In the static method of analysis, the deflection Scaused by shifting the large balls is measured between the two equilibrium positions. If the scale is distant Lfrom the mirror, then S/Lis twice the angle qthrough which the system has turned. To convert this angle into torque, the torsion constant t0 (defined as torque per unit angular deflection) of the suspension wire is found indirectly from the suspended system's moment of inertia Iand its period T when oscillating as a torsion pendulum.Change in torque due to gravitation = change in torque of suspension.

The major systematic error is introduced by the attraction of the opposite balls.For the measured values this correction gives G = 6.75 x (10 exp -11 nt.)(msquared) (kg exp -2) + 2%. This is in satisfactory agreement with the accepted value. Several other small systematic errors happen to cancel out.