Theoretical Mechanics

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Theoretical Mechanics
Hoskins, Leander Miller, 1860-
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S. units.
MOTION IN A STRAIGHT LINE: APPLICATIONS. 20I § 4. Miscellaneous Problems.
233. Constant Force Combined With Central Force. — Let a body be acted upon simultaneously by a constant force and a force directed toward a fixed point. Then if P^ and P.^ are the values of the two forces at any instant, the general equation becomes mx^P. + P,, . . . . (i) and we must put for /\ and P^ their values as functions of x and /.
If the origin is taken at the center of force, and the central force is
...a function of the distance from the center, we have P, = constant ; P^ = f{x).
The only case that will be discussed is the following : Body suspended by elastic string, — A body is suspended from a fixed point by an elastic string, and is acted upon by no force except its weight and the supporting force exerted by the string. To de- termine the motion.
We must here make use of the property that a stretched elastic string exerts a resisting force proportional directly to the amount of stretching.


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