SM052     Analytical Balance     circa 1962     Mechanics    

  The balance is an instrument for determining the relative weights or masses of bodies.   The ordinary balance consists of a lever of the first kind, called a beam, with the fulcrum in the middle and a scale pan on each extremity.   The fulcrum consists of a steel knife fixed to the beam resting on flat agate supports to diminish the friction.   A needle or pointer swings on a graduated scale indicating balance in the centre position.

  A balance must satisfy the following conditions:

   (i)                 Two arms to be precisely equal in length.

(ii)              Balance to be in equilibrium with scale pans empty.

(iii)            With the beam horizontal, the centre of gravity to be in the same vertical plane with the edge of the fulcrum and a little distance below, to achieve stable equilibrium.

The balance is delicate or sensitive when a small difference between weights in the pans causes a sensible deflection of the pointer.   If  P and Q are the weights, 2a is the length of the beam and height of centre of gravity is h, then if W is the weight of the beam:

  where    θ     is the angle turned by the beam.

The method of double weighing is a means of accurately determining the weight of a body even with a non-accurate balance.   To do this the weight of the body is balanced against lead shot or sand and then it is replaced by known weights to restore equilibrium.