Mathematical Problems and Examples; Arranged According to Subjects, from the Senate-House Examination Papers, 1821 to 1836 Inclusive

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 edition. Excerpt: ...about one extremity; find the tendency of the cis inertize in any given position to bend the rod at any point, and determine at what point that tendency is the greatest. 151. A body is oscillating in a cycloid, in a medium where the resistance varies as the (vel.)', and the density varies inversely as the arc measured from the lowest point; prove by a method similar to Newton's in Book II. Prop. 26, that the time of descent to the lowest point will be the same from all altitudes; and apply the integral calculus to find the whole time, supposing the resistance at the highest point corresponding to 'ii, where z is the length of the any velocity v, to be less than I pendulum. 152. Find the limit of the velocity communicated by a body A to C, through an indefinite number of mean proportionals between A and C, the bodies being supposed perfectly elastic. I53. Explain D'Alembert's principle, and apply it to determine the motion of two bodies connected together by a wheel and axle; the inertia of the machine being taken into account. 154. The heights of the ridge and caves of a house are H and /2, and the roof is inclined at 30 to the horizon. Find where a sphere rolling down the roof from the ridge will strike the ground, and also the time of descent from the eaves. 155. A river, of which the breadth is a, flows with a velocity u, and a swimmer, whose velocity is nu, always aims at a mark on the farther bank directly opposite to the place where he entered the river. Find the curve in which he swims, and shew that the time of his arriving at the mark is equal to l56. A uniform rod, of which the elasticity is e, falls upon a smooth horizontal plane: given the altitude from which it falls, and its inclination to the...show more

Product details

• Paperback
• 189 x 246 x 4mm | 163g
• United States
• English
• black & white illustrations
• 1236896297
• 9781236896292