Cavendish experiment

The gravitational scale is the measuring instrument in a physical experiment (also known as the Cavendish experiment ) to determine the gravitational constant, which determines the strength of the gravitational attraction between masses. So you are on a measure of the strength of gravity.

Henry 1798 Cavendish used such an apparatus to the first time able to determine the density of earth. Although Cavendish himself was not interested in the gravitational constant, succeeded by his experiment to calculate their value even remotely accurate.

Construction

Essentially, it involves a torsion balance, as it is also used in applied geophysics. " Torsion balance " means that the magnitude of the angle through which a wire is rotated from its rest shape, provides information about the applied torque. From this it can be the force acting between the test masses compute power.

Specifically: In the middle of a wire on which a horizontal bar is attached depends. This mirror are fixed ( parallel to the wire ) and two small masses at the ends in the center. Before there is a light source (now usually a laser ) emits a relatively narrow beam of light. This is directed to the wire, and is reflected by the mirror to a narrow remote screen. Now is a deflection of the mass from the rest position rather than, one can determine this by means of a displacement of the light spot imaged.

Experiment

Preparation:

• You have to know the lever length, distance to the screen and the ground.

Implementation:

• We positioned two large masses in the same distance from center of mass to center of mass, which should be as perpendicular as possible to the bar.
• The masses and on the opposite sides of the experiment on back and the rod rotates slightly, after which he falls into a damped torsional vibration microscopic scale. It is observed as the light spot imaged levels off at a different distance to the point from the rest position.
• This distance is measured (and optionally the period of oscillation ).
• We repeated the experiment with other masses and distances to reduce errors.

Account

The following calculation is valid under the condition of small distances r between large and small masses. Only then arises from the gravitational attraction between these two spheres a force acting substantially perpendicular to the bar ( where the small masses are suspended ). Then the result for the torque.

Torque: The attraction force of the mass causes a torque to the rod. Strictly speaking, there is also an opposite torque which is due to the large balls further away by the attraction of the small balls. Of rotation by acting against the strength of the wire, the greater the angle of rotation θ, the more resistance there. This reaction is approximately proportional to the angle, the proportionality factor is called Directorate moment.

Oscillation frequency: Within the range of the linear approximation torsional vibrations are harmonic and its angular frequency is only dependent on the Directorate torque and the moment of inertia. The latter is calculated here simply as. It follows from the oscillation period. So is.

Deflection: As in all of the mirrors of the image rotation angle is twice as large as the rotation angle of the mirror. Assuming a slightly curved screen, so the angle at which the wire has been rotated.

Equilibrium: The equilibrium between attraction and considerate driving force must be applied. So. Now the gravitational constant can be calculated by merely forming,

If the distance to the screen is equal to the length of the lever, so results

Relevance

The excessively appearing effort is mainly explained by the weakness of gravity. Nevertheless, some schools and all physics institutes have such an apparatus. In a self-built equipment but a relative error of 20 % is quite a good performance.