New PDF release: Applied Mechanics - Dynamics

By Housner G & Hudson D

1950 - utilized Mechanics Dynamics, by way of George W. Housner & Donald E. Hudson (Division of Engineering, California Institute of Technology), D. Van Nostrand Co., Inc., Toronto, N.Y. & London

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Extra info for Applied Mechanics - Dynamics

Example text

We may thus state that the total momentum is a constant : mava + mbvb = constant If there are more than two particles involved and all the forces acting upon the particles are due to mutual interactions, that is, there are no external forces applied to the system, we can say: Cmlvt = constant This is a vector equation and in rectangular coordinates its components are: Em& = constant, etc This is the Princi\$le of the Conservation of Momentum, which holds for any system upon which no external forces are acting.

Assume there is no air resistance. (b) Suppose the projectile of part (a) were subjected to an air resistance proportional to the velocity squared; that is, the magnitude of the retarding force is kv2 lb. Apply dimensional analysis to obtain an expression for the range. 7. Using the method suggested in the text, show that if the ratio of two measured values of a secondary quantity is independent of the sizes of the fundamental units used, the secondary quantity must have the form of the product of powers of the primary quantities.

17. Referring to the helicopter blade of Example 3 above, find the acceleration of the blade tip A when the angle 4 has one-half of its maximum value t\$o = 6" and is increasing. The "coning angle" 0 is 7", the radius to the tip of the blade is rl = 15 ft, the radius of the disk is R = 1 ft, and the assembly rotates at 225 rpm. The blades flap once per revolution of the rotor, that is, p = w . 18. A horizontal track for experimental studies of high velocity missiles is to be designed. Because of the rotation of the earth, there would be, for certain orientations of the track, accelerations at right angles to the rails in a horizontal plane, and hence lateral forces between the missile carriage and the track would be present and might be a factor in the design of the structure.