Text-Book of Mechanics Volume 2 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 Excerpt: ...From the general value for the velocity derived in the above example obtain the time t required to fall a distance s. Exercise i76. Determine the time it would take a particle of mass m to reach a center of force attracting it with a force varying inversely as the square of the distance of the particle from the center of force if the particle starts from rest at a distance b from the center. Exercise i77. A particle moves in a straight line subject to an attraction proportional to s. Show that the velocity acquired in falling from an infinite distance to the distance b is equal to that acquired in falling from rest at b to a distance--from the center of attraction. MOTION OF A SYSTEM OF CONNECTED TRANSLATING BODIIS In this section we will consider the accelerations and stresses existing in a system of non-rigidly connected masses whose only motions are translations. In these problems we will consider the pulleys involved as massless and their pivots as frictionless, so that no force is required to turn them. This is equivalent to saying that the tensions in the strings passing over such imaginary pulleys are equal on both sides of the pulleys. The method of procedure in problems involving the motion of non-rigidly connected masses is as follows: 1st. Represent the unknown tensions and accelerations by letters. 2d. Find the relation existing between the accelerations involved owing to kinematical reasons. The equations so obtained are called Kifiematic Equations. 3d. Consider each mass as a "free body" and apply the equation of motion to each. The equations thus found are the Kinetic Equations. 4th. See that the number of equations equals the number of unknown quantities. If the equations are too few in number, Static Equations must exist at some m...