Mathematical Problems and Examples, Arranged According to Subjects, from the Senate-House Examination Papers, 1821 to 1836 Inclusive (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.1836 Excerpt: ... SECTION XV. QUESTIONS IN PURE DYNAMICAL SCIENCE, NOT INCLUDING CENTRAL FORCES. 1. Find the law of force by which a body may describe a rectangular hyperbola, the force acting in parallel lines perpendicular to one of its asymptotes. 2. Two pendulums, the lengths of which are L and /, begin to oscillate together, and are again coincident after n oscillations of the first pendulum. Given L to find I. 3. In what direction must a body be projected with a given velocity from a point in a given inclined plane, that the range may be the greatest possible? 4. Two bodies are projected from two given points in given directions and with given velocities; find their distance at the end of t." 5. A rod is placed in an inclined position, with one end upon a perfectly smooth horizontal plane; find the equation of the curve described by the other extremity whilst it falls. 6. Explain what is meant by accelerating force; and when P draws up Q in a machine, find the force accelerating Q's ascent, both when P and Q move with the same and with different velocities, the inertia and friction of the parts of the machine not being considered. 7. Two equal bodies A and B are connected by a string of given length: A is placed in a horizontal groove, and B hangs freely down, the string passing through an aperture which is continued along the bottom of the groove: a given velocity is given to A; find the position of B at the end of tn. 8. A body descends by gravity, and describes in the nih second of its fall a space = p times the space described in the last but n; required the whole space. 9. Mention some of the experiments and observations, from which we may infer the truth of the second law of motion. 10. A given globe rolls down a given inclined plane in a medium resisting as the ...