W

The centres of oscillation and percussion are in the same point. If a heavy straight bar, of uniform density, be suspended at one extremity, the distance of percussion is two-thirds of

its length.

In a long slender rod of a cylindrical or prismatic shape, the centre of percussion is nearly two-thirds of the length from the axis of suspension.

In an isosceles triangle, suspended by its apex, the distance of the centre of percussion is three-fourths

rod whose density varies as the distance from tide. In a line or

point of suspension, also in a fly-wheel, and in wheels in general, the centre of percussion is distant from the centre of suspension three-fourths of the length. In a very. slender cone or or pyramid, vibrating about its apex, the distance of its centre of percussion is nearly four-fifths of its length. IN 2 MP gi

OnWork.

A unit of work is one pound avoirdupois raised vertically one foot. If U denotes the units of work in raising W lbs. A feet preisk

Rule to find the Units of Work in Raising a given Weight a given Height.

Multiply the height in feet by the weight in pounds, the product will be the units of work done.

EXAMPLE Find the units of work in raising half a ton 30 feet high.

.. U = 1120 × 30 = 33600 units of work.

It is important to observe, in the application of the above for mula to practical cases, that the height () is the vertical distance through which the centre of gravity of the body whose weight is (W) is raised.

EXAMPLE. Find the units of work in lowering the surface of water in a well one yard; the depth to the surface of water eing 40, and diameter 3 feet.

The weight of a cubic foot of water is 624 lbs.

The weight of water

9 x 7854 × 3 × 62.5=1325.36 lbs The height through which the centre of gravity is raised 415 feet.

.. U=1325·36 × 41·5 = 55002 units of work.

or any

The work done in raising a body up an inclined plane, curved surface, is equal to the work done in raising the body ver tically through the height of the inclined plane.

There are 29000 units of work done in sawing a square foot of green oak.

Units of Work.

Put H, equal to

horse power is 38000 units of work done in one minute. «'}
horse power, and U, the units of work done,
ma bookbailey 4 Ü her gabants weal & ek

in Thours:

33000 H

60 T

The following results are taken from MORIN:

A Man laboring Eight Hours per Day will perform the following

Pushing and drawing alternately in a vertical direction,

A Man laboring Six Hours per Day.

4250

3120

2380

2600

4000

Raising material with a pulley

Raising material with the hands,

1470

Raising material upon the back, and returning empty..

Raising water from a well with a pail and rope,

EXAMPLE. Required the horse power of an engine that will saw 368 planks, each being 30 feet by 2 feet 6 inches, in twelve hours

There are 29000 units of work done in sawing one square foot;
Then 30 x 2.5 × 368 × 29000 =

EXAMPLE. How many tons of coals would two men raise, working with a wheel and axle, from a pit whose depth is 20 yards, in 12 hours?

督

From the Table, a man working with a wheel and axle will do 2600 units of work in one minute.

Then, 2600 × 60 × 12 x 2 = work done by the two men.
Put the tons of coals raised.

Then, 2240 x 20 × 3 × x = work done by the two men.

.x=

2600 × 60 × 12 × 2

2240 × 20 × 3

27.85 tons raised.

The Traction of Horses at various rates of Travelling. It is a well known fact, that the traction or force which a horse can exert decreases with the increase of speed.

Accumulated Work

31 4 41 5 104, 83, 621, 417.

If a force be applied to move a body subject to no resistance whatever, it will be wholly occupied in increasing the speed of the body. In this case the work which is done by the action of the force applied is accumulated in the body, therefore it is called accumulated work.

Put V = the velocity of the body or feet per second.

And W:

the weight of the body in pounds.

If W be measured in tons, and V be measured in miles per hour,

A railway train 80 tons moves uniformly at the rate of 30 miles per hour, find the accumulated work.

77 W V2

=

where W

33750

Generally the horse power of the engine

is in tons and Vin miles per hour.

The friction of a railway train is from 8 to 10 lbs. per ton,

Work done by Machines.

The moving power, which is applied to any machine moving uniformly, is employed in overcoming the resistance of friction, and useful work done at the working points of the machine. Hence,

units

the aggregate number
rate number of un of useful work yielded by any
machine at its working point is less than the number received upon

the machine upon the stance Power, by, the number of

units expended

moving uniformly.) di qd anob show

General Rule to find the Work

of friction. (The machine

Work done by any Machine,

Find the distance through which the power (P) applied to the machine has travelled in one minute, and let this distance be called (a).

Find the distance through which the weight. (W), producing useful work, has travelled in one minute, and let this distance be (b). Then a P-b W= work done by And a P

done by friction per minute.

work applied per minute.

W useful work done per minute.

The Horse Power of an Engine.

Let P be the mean effective pressure of the steam on the piston. be the length of the stroke in feet.

en be the number of strokes per minute.

Aod tog crím ví fơn the Strength of Animals.mp

Let P be the force in lbs. that any animal can exert when moving at (v) miles per hour.

Put the greatest effort the animal can exert when standing. the greatest number of miles per hour the animal can give itself when unimpeded by any weight.

And c =

It is readily seen that (v) miles per hour is equal to (88 v) feet per minute. Put U the units of work done by the animal per minute,

Then, according to Bouguer, U = 88 (v - 2). K.

when

The values of U will be the greatest bollaya ma

Substitute these values in the formula for P and U, then there will result:

K

2K

the load of the animal when producing the greatest effect.

4K

9

22 c Kthe greatest effect, by first formula.

To Calculate the Different Parts of a Crane as respects Mechanical Advantage.

(1.) The number of revolutions of the pinion to one of the wheel, the length of the handle, and the force applied being given, to find the diameter of the barrel.

RULE. Multiply the diameter of the circle described by the winch, or handle, in inches, by the power applied in lbs, and by the number of revolutions of the pinion to one of the wheel; divide this product by the weight to be raised in lbs., and the quotient is the diameter of the barrel in inches.