Let w denote the weight per unit length of the chain, then the weight of the chain has magnitude

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

Restated in mathematical terms, on the surface of the Earth, the weight w of an object is related to its mass m by w

where w is the weight of the collection of similar objects and n is the number of objects in the collection.

The position k is the logarithm of the corresponding weight w, that is.

The number of tally marks required in the unary numeral system for describing the weight would have been w. In the positional system, the number of digits required to describe it is only, for.

Its weight, F < sub > w </ sub >, depresses the surface, and is balanced by the surface tension forces on either side, F < sub > s </ sub >, which are each parallel to the water's surface at the points where it contacts the needle.

where w ( x ) is a weight function, and represents complex conjugation, i. e. for.

The definition can be extended further to tensor densities of weight w for any real w. If T is such a tensor density, then its Lie derivative is a tensor density of the same type and weight.

Polymers can be characterized by a variety of definitions for molecular weight including the number average molecular weight ( M < sub > n </ sub >), the weight average molecular weight ( M < sub > w </ sub >) ( see molar mass distribution ), the size average molecular weight ( M < sub > z </ sub >), or the viscosity molecular weight ( M < sub > v </ sub >).

The street that is full now of traffic and parked cars then and for many years drowsed on an August afternoon in the shade of the curbside trees, and silence was a weight, almost palpable, in the air.

The weight of fame and history is formidable, and dreary steel engravings in schoolbooks do little to quicken interest and imagination.

He feels, suddenly, the weight of the fat that is on him.

The only hope which good teachers have for being paid their due is to stop dragging the dead weight of poor teachers up the economic ladder with them.

The only fact that holds any weight in the article is the result of the tea party.

But for purely definition purposes -- used in conjunction with your regular Squatting, Leg Curling, Leg Extensor programs -- a heavy weight is not needed.

A tire must be inflated to its normal hot operating pressure and the car must be loaded to its operating weight when this measurement is made.

Marlin's latest is also designed for the beginning shooter, although it's a full-sized rifle with plenty of barrel weight and ample stock.

By lifting the seat upwards a little, the weight is taken off the neck and the back is kept rounded.

The expected weight loss for Af going to Af and Af is 10.6%.

As is well known, detergent actives belong to the chemical class consisting of moderately high molecular weight and highly polar molecules which exhibit the property of forming micelles in solution.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

-- One of the principal aims of anionic polymerization techniques is the synthesis of polymers of extremely narrow molecular weight distribution.

Upon completion of the purging step, additional initiator appropriate for the molecular weight of the sample desired is added, and the system is then warmed to the polymerization temperature, at which the reaction is allowed to go to completion.

To understand American politics is, simply, to know people, to know the relative weight of names -- who are heroes, who are straw men, who controls, who does not.

The appestat, which adjusts the appetite to keep weight constant, is located, says Jolliffe, in the hypothalamus -- near the body's temperature, sleep and water-balance controls.

Scientists assume that cholesterol ( from the Greek chole, meaning bile, and sterios, meaning solid ) is somehow necessary for the formation of brain cells, since it accounts for about 2% of the brain's total solid weight.

* The Omotic language branch is the most controversial member of Afroasiatic, since the grammatical formatives which most linguists have given greatest weight in classifying languages in the family " are either absent or distinctly wobbly " ( Hayward 1995 ).

The 1 / 4 abacus, which is suited to decimal calculation, appeared circa 1930, and became widespread as the Japanese abandoned hexadecimal weight calculation which was still common in China.

An aardvark's weight is typically between.

The mixture is roughly half sand ( 50 %), one-third clay ( 35 %), and one-sixth straw ( 15 %) by weight.

When building an adobe structure, the ground should be compressed because the weight of adobe bricks is significantly greater than a frame house, and may cause cracking in the wall.

He pulled it over, climbed up, and lifted out the big volume, almost losing his balance from the weight of it.

Quantitative analysis is achieved by measurement of weight or volume.

A number of harmful and undesired ( adverse ) effects have been observed, including lowered life expectancy, extrapyramidal effects on motor control – including akathisia ( an inability to sit still ), trembling, and muscle weakness – weight gain, decrease in brain volume ( although this is being debated, since schizophrenia, which is often treated with antipsychotics, also causes a shrinkage of brain volume ), enlarged breasts ( gynecomastia ) in men and milk discharge in men and women ( galactorrhea due to hyperprolactinaemia ), lowered white blood cell count ( agranulocytosis ), involuntary repetitive body movements ( tardive dyskinesia ), diabetes, sexual dysfunction, a return of psychosis requiring increasing the dosage due to cells producing more neurochemicals to compensate for the drugs ( tardive psychosis ), and a potential for permanent chemical dependence leading to psychosis worse than before treatment began, if the drug dosage is ever lowered or stopped ( tardive dysphrenia ).

If weight is added to the boat, the volume below the waterline will increase to keep the weight balance equal, and so the boat sinks a little to compensate.

Furthermore, in the case of the obese woman, a breast lift ( mastopexy ) procedure, with or without a breast volume reduction, can be part of an upper-body lift and contouring for the woman who has undergone massive body weight loss.

By volume and weight, the largest concentrations of crystals in the earth are part of the Earth's solid bedrock.

In some cases ( for instance, in the United States oil and gas industry ), density is also defined as its weight per unit volume, although this quantity is more properly called specific weight.

Further, density may be expressed in terms of weight density ( the weight of the material per unit volume ) or as a ratio of the density with the density of a common material such as air or water.

; Unit Weight: Total unit weight: Cumulative weight of the solid particles, water and air in the material per unit volume.

Brass cases can be matched by volume, weight, and concentricity, bullets by weight and design, powder charges by weight, type, case filling ( amount of total usable case capacity filled by charge ), and packing scheme ( characteristics of granule packing ).

The quantity of gunpowder is specified by weight, but almost always measured by volume, especially in larger scale operations.

When using volume to meter each charge, it is important to regularly check the charge weight on a scale throughout the process.

Such products reduce the use of raw materials for framing and stuffing and reduce transportation weight and volume to about 15 % of that of conventional furniture ;

A List of knapsack problems # Multiple constraints | multiple constrained problem could consider both the weight and volume of the boxes.

Its design enabled construction of lenses of large size and short focal length without the weight and volume of material in conventional lens designs.

Synthetic polymers may consist of both crystalline and amorphous regions ; the degree of crystallinity may be expressed in terms of a weight fraction or volume fraction of crystalline material.

Especially for carrying around data, the weight and volume per MB are relevant.

On the other hand, written and printer paper do not require ( the weight and volume of ) reading equipment, and handwritten edits only require simple writing equipment, such as a pen.