# The Cambridge Course of Elementary Natural Philosophy; Being the Propositions in Mechanics and Hydrostatics in Which Those Persons Who Are Not Candidates for Honours Are Examined for the Degree of B.A.

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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. 1864 edition. Excerpt: ...are parallel, if the weight of the pulleys be regarded, under what circumstances will the mechanical advantage be reduced to The weight of the upper block will have no effect, because it is supported, by supposition, from without. But the weight (w) of the loiter block will add to the weight W, and the result, in case of equilibrium, will be P: W+w:: 1: n, the number of strings at lower block;.-. W+w = nP, or =n--which becomes 0, when w--nP; that is, the mechanical advantage is nothing, when the weight of the lower block is equal to, or greater than, the power multiplied by the number of strings at the lower block. 18. In Prop. XIV, (Art. 45), find the inclination of the plane, when the pressure of W on the plane is equal to P. In the triangle DEF, DF represents the power, FE the weight, and DE the pressure on the plane; therefore the pressure on the plane is equal to the power, when DE= DF. But DE: DF:: AC: BC; therefore the pressure =P, when AC=BC, or Labc=lbac, ' i. e. when the inclination of the plane equals half a right angle. 19. A weight of 20 lbs. is supported on an Inclined Plane by means of a string fastened to a point in the plane; and the string is only just strong enough to carry a weight, hanging freely, of 10 lbs. The inclination of the plane to the horizon being gradually increased, find when the string will break. As long as there is equilibrium, the tension of the string is represented by P in Prop. XIV; and P: W:: height of plane: its length. Now, as the inclination of the plane is increased, the height is increased, and P also; and when P exceeds W, or 10 lbs., then the string breaks, that is, when the height of the plane first exceeds half its length. 20. Prove that a body may balance in two. positions round a line, which...