matter if a body (or projectile) falls straight to earth or falls in a different path because of an outside force. The time may be more, but the fi nal velocity will be the same. If a body is thrown downward, (or a projectile is fi red
downward) to the constant force already found must be added the impulsive force given the body. This is proportional to the velocity imparted and the time of its action. In other words, the velocity at impact would be the total of the two. If a body (or a projectile) is launched upward, the direc-
tion of the body is opposite to gravity and its velocity will be diminished each second by the quantity g = 32.17. Therefore, the time of rise will be found by dividing its original velocity by g.
Remember that in all of these cases the actual fi gures
are never realized in practice because of air resistance and other variables. If we raised a 50 lb. weight to 10 ft., we would expend
500 ft. lbs. or a 10 lb. weight to 30 ft. we would expend 300 ft. lbs. Weight times the number of feet equal foot-pounds. If the 50-lb. object fell the 10 feet, the kinetic energy is the energy of the object in motion during the fall. All objects in motion have kinetic energy. kinetic energy = MV2
/ 2
Where: M = mass V = velocity
For bullets use: energy in ft. lbs. = WV2
Where: W = weight of bullet in grains. V = velocity in feet per second.
For readers who have followed ballistics in other publi-
cations or studied kinetic energy in school, a brief explanation is required at this point. The formula for energy can be found with both 450,240
and 450,400 as the denominator. Also the gravitational con- stant is seen as 32.2 and 32.16 and 32.17 and perhaps a few others as well. The key is the gravity constant because the long number in the denominator is related to it. The pull of gravity is not the same at different locations. It is the strongest on the earth’s surface and less above it and
/ 450400
below it. Even on the surface it will vary. Example: 32.258 ft./sec. at the poles and 32.144 at the equator. The variation is slight, as is the variation of calculations using the different fi gures.
Gravity is the term for the attraction between material
bodies. The Newtonian law of universal gravitation declares that every mass attracts every other mass with a force, which varies directly as the product of the attracting masses and inversely as the square of the distance between them. In actuality, the earth is not a sphere. Its shape is closer
to a spheroid whose equatorial radius is 21.6 kilometers longer than its polar radius. Also it rotates and the centrifugal force due to rotation reduces gravity, especially near the equator. The earth’s surface is also irregular in outline and the density variable, at least near the surface. Thus the formulas for the variation in gravity at different parts of the earth’s surface are complicated. For years, 32.2 was used for basic calculations and 32.16
or 32.17 for advanced calculations. Lately, the standard value of 32.1741 ft./sec. has been set by international agreement. This makes the more simplistic 32.17 the number to use. The denominator of 450,240 was correct for a gravity
value of 32.16. Using the gravity value of 32.1741 the denomi- nator works out to 450,437.4 and with 32.17 it is 450,380.0. For ballistic purposes, the modern trend is to use 32.17 ft./ sec. squared for the gravitational constant and 450,400 for the denominator in energy formulas. In any case, the difference in the fi nal result is so slight that you probably are wondering why I went to the trouble to discuss it. (At this point, so am I.) This long number is the energy factor or the 1 / 2 M in
some energy formulas. To obtain, use the formula: 1 / (2 * g * 7000). The digit 2, because we must either multiply by 1 / 2 or
divide by 2, and the 7000 is the number we divide the grains of the bullet’s weight to obtain pounds. Therefore: 2 * 32.17
* 7000 = 450,380. Weight and mass are not the same, although most
Americans without a background in engineering or phys- ics may believe they are. People who use the metric system have an easier road to understanding. They use the kilogram for mass and the newton for force or weight. In the English system of physics, mass is weight in pounds divided by the acceleration of gravity, 32.17. To be technical, in engineering terms the pound is not
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a unit of weight but of force. The slug is the term used for mass. For some, slug conveys a mental picture of a bullet. Other readers may think of a piece of metal used in place of a coin in a vending machine or of a small snail-like creature with no shell. To printers of an earlier generation, it is a strip of type from a Linotype machine. The slug is also called the geepound or the engineer’s unit of mass. (The English language is strange at times.) In physics, a slug is the mass that an unbalanced force
of 1 lb. will create an acceleration of 1 ft./sec. squared. Let us word it slightly differently and yet say the same thing. A force of one pound will accelerate a mass of one slug one foot per second per second. In other words, an object with a mass of 1 slug is accelerated on the surface of the earth at 32.17 ft./sec. squared by gravity. The pull on the object would be 32.17 lbs., which would be its weight. This brings us back to the
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