Vol. 5. No. 2.

CHICAGO, NOVEMBER 10, 1918.

$2.00 Per Year

PART I.

The vibrations of a beam in a platform scale have often been compared with the movement of a pendulum in a clock Both have evidently a motion which is not perpetual, the clock will come to a stop when the spring or the weight ceases to act, also the scale beam will come to rest when an over weight appears or friction between moving parts exceeds the expended force, by which the vibrations were started. In general a pendulum is a body swinging or oscillating about a fixed point. The simple deal or mathematical pendulum is a weigh less line or wire, pivoted at the apper end and carrying a bob at the Lower end When disturbed from its vertical position, oscillations or beats take effect, whose duration or period depends upon the length of string or wire by which the bob is suspended and the attraction of the earth. A not moving pendulum is therefore held in vertical position by the power of the earth. Impulse of motion and friction exhausted self, until the attraction of the earth grows larger and commands the state of repose. During the performance, from pressure of bob, wire and friction upon bearing heat and wear are generated, compensating in this manner the exer

Oscillations In Scales

By EUGENE MOTCHMAN
Mechanical Engineer

Standard Scale & Supply Co., Pittsburgh, Pa.

The power of attraction causes all free and unsupported bodies to tail to the earth at varying speed, the farther the object from the surface the smaller the attraction, approaching the earth the speed increases. A falling body under the action of gravity alone, is a case of uniformly accelerated motion, amounts to 16.16 feet per second and acquires a speed of 32.2 feet per second at the end of first second. The force of gravity

varies slightly at different latitudes, at 45 degrees the velocity for the first second of descent is 16.083 feet. For practical purposes the following table shows the velocity of time (t), distance fallen through in feet (h), velocity acquired at end of time in feet (v) and space fallen through in last second of fall in feet (s).

A scale beam under impulse of over weight also falls some small distance which rarely exceeds 2 per cent of long arm, and suffers acceleration which must be considered with the constant "g" equal 32.2, appearing in all time-formulae on oscillations under the action of gravity.

For the simple pendulum the time of oscillation is depending upon the length of string and this accelaration "g", the weight of the bob is immaterial.

Then (1) t = pi (L/g)1.

When "t" time in seconds of one passage from right to left or reverse, pi the constant of a circle radius one (1) == 3.14 and L the length in feet, index 2 indicates the square root to be extracted from the fraction (L/g) and also in following formulae.

A pendulum 9 feet long will beat: t = 3.14 (9/32.2) 3.14 X .53 = 1.7 seconds.

The length of a simple pendulum from its point of suspension to the center of gravity of the bob is directly proportional to the square of the time for one beat:

Thus, 9:2.89 3.12:1.

Let 9 the length of pendulum in feet 2.89 the square of 1.7 seconds 3.12 ft. the length of second pendulum 1 the time of beat in seconds.

To obtain a normal pendulum which will beat exact seconds, it must be:

(2) L = "/pi1

numerized: 3.26 ft. 32.2/9.86 or 39.12 inches.

(3) t = 2 pi (K2/dg)'

When K the radius of gyration, "d" the distance of center of gravity from center of rotation, other smybols as before.

From the square of the radius of gyration K and d, a dignity is created by dividing, K' with the distance "d" only. The quotient is a mathematical quantity of great usefulness and importance. This dignity is the radius of oscillation "r", its function and relation is the proportion:

Remove beam from scale, weigh it with balance ball and poise but without loops exact to 4 ounce, this quantity is called A and weighs 2.44 lb. Next weigh the counterpoise and its loop at the tip of beam as it balanced scale complete, name it C .89 lb. Measure within 1/100" the long arm of beam "1" 121⁄2 inches also the short arm "f" 21⁄2 inches. To find the weight B return the beam with loops and counterpoise to its place in scale, from the butt loop at end of beam from pivot "a" pass a chord through pillar and hang ballast to it until the beam oscillates with counterpoise at the other end, but without levers and platform, the poise, of course, points to zero. Ascertain now the weight of the ballast, chord and butt loop it will be B 6.34 lb. To find the center of gravity "h" of this combination, beam A and Counterpoise C without B at opposite end experimentally, secure a triangular file and balance the combination upon it as seen in Fig. 1, then measure from the corner of file horizontally to the edge of pivot "c" and name this distance "d". Likewise

(6) h=Bg/A+C 4.76 inches from c. This result will coincide the practical The experiment upon triangular file. center of gravity of beam and poise alone is determined by experiment upon triangular file or by the following method: s like the following:

Square root of difference B (f + d)' minus C n' divided by A plus B, see Fig. 1, where "n" the distance from center of gravity "h" to pivot 6, expressed by formula:

1. Moment of inertia of a body.

This quantity is difficult to prepare from dimensions of irregular shaped bodies, and more so from a combination as demanded in this case. A maximum moment of inertia which meets all following conditions and deductions in sense of accepted practice is: (8) I As'+Bf+ Cl2 + (A + B + C) d' Applied 8.88 +39.62 + 139.06 +219.02 I= 406.58 lb. inches squared.

As seen the moment of inertia contains the effective weights A, B and C at proper distances from rotation center plus the entire mass about center of gravity "h" by distance d'.

2. Radius of Gyration.

The center of gyration "i" is that point of a rotating body at which the entire mass, beam and weights possesses the

1-12.5" T= 12.67.

balance the beam only (2.44 lb.), and locate the center of gravity "s" to 1.91" from pivot c, which is also known as the center of rotation. The weights A, B and C produce 3 distinctly different centers of gravity s, h and c whose position can be definitely determined in any case. By calculation from known data the center of gravity "h" can be found by the equation of moments about pivot "c" from known items.

C 6.89 Lb

PS45%

same energy as at point of rotation, it cannot be at the centers of gravity c, s and h nor at the center of oscillation, but lies on a straight line between center of gravity and center of oscillation. This radius of gyration K is the distance from center of rotation to center of gyration. Then is the square of this distance K an average of all distances from "c" to each elementary particle and weight of the combination (beam,