This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.

If a body falls freely in vacuum, that is, without resistance from the air, its velocity will not be constant throughout the entire fall, but will increase at a uniform rate. This uniform increase in speed is called the acceleration of gravity. It is expressed in feet per second per second.

Fig. 36. Mercury Plumb Bob.

When a body falls freely in this manner it will have attained at the end of one second a velocity of 32.2 ft. per second. Thus the average velocity during the first second will be 16.1 ft. per second. Since the velocity increases at a uniform rate, it will be 64.4 ft. per second at the end of 2 seconds, and the space fallen through during this second second will be 48.3 ft.

The average velocity of the object for any second is the average of the velocity at the beginning and the velocity at the end of that second.

Thus:

Velocity at beginning of 1st sec. | = | 00.0 | ft. per sec. | ||

Velocity at end of 1st sec. | = | 32.2 | " " " | ||

2) | 32.2 | ||||

Average velocity for 1st sec. | = | 16.1. | " " " | ||

Velocity at beginning of 2nd sec. | = | 32.2 | " " " | ||

Velocity at end of 2nd sec. | = | 64.4 | " " " | ||

2) | 96.6 | ||||

Average velocity for 2nd sec. | = | 48.3 | " " " | ||

Velocity at beginning of 3rd sec. | 64.4 | " " " | |||

Velocity at end of 3rd sec. | = | 96.6 | " " " | ||

2) | 161.0 | ||||

Average velocity for 3rd sec. | = | 80.5 | " " " |

As the space fallen through in any given second is equal to the average velocity for that second, it follows that the total distance fallen through at the end of any given second is equal to the average velocity up to the given point multiplied by the number of seconds during which the object has fallen.

For example:

Initial velocity | = | 00.0 | ft. per sec. | |

Velocity at end of 3rd. sec. | = | 96.6 | " " " | |

2) | 96.6 | |||

Average velocity for first 3 sec. | = | 48.3 | " " " | |

3 X 48.3 = 144.9 ft., space fallen through in first 3 sec. |

The above theory supposes a body to be falling freely in a vacuum, but while the air will offer a resistance and somewhat reduce the actual motion the principle is the same. Acceleration due to gravity varies but little at different latitudes of the earth. Acceleration due to gravity decreases at higher altitudes, and increases as we go below the surface of the earth. All these variations on the earth's surface are so small that they hardly need to be considered in any calculation concerning practical problems in mechanics. Acceleration due to gravity may be considered as 32.2 ft. per second each second.

Since the velocity of falling bodies increases at the uniform rate of 32.2 ft. per second, the final velocity in feet per second must equal the product of the time in seconds multiplied by 32.2.

To illustrate the calculation: What final velocity will a body acquire in a free fall during 7 seconds?

V = 7 X 32.2 225.4 ft. per second

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