# The Student's Mechanics

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## Description

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. 1883 edition. Excerpt: ... Let A C, the height of the plane, equal h, and A B, the length of the plane, equal I. Then t h If the body be projected up the plane, the retardation due to the body's tendency to fall will also be represented by ac, and will be equal to yxj, The motion of the body, if allowed to fall down the plane, can be ascertained by putting f= j g (or f= g sin a) in the equations =/; -=2-; 0-2/8. If the body be projected up or down the plane, the motion can be determined by substituting this value of/in the equations 319. Problem.--To find the velocity acquired by a body in Jailing down a given inclined plane. Let A B be the inclined plane, a its inclination, P the place of the body at a given time, B P = 8, v = the velocity at P; then we have by our formula, since u = o, v2=2g sin ax s, FlS-52-which gives the velocity. If we draw B C perpendicular to the horizontal line through A, and call V the velocity at A, we have V = 2g. A B sin a = 2g. BC. Hence the velocity is the same at A, as if the body had fallen through the vertical space B C: that is to say, the velocity generated by gravity depends solely upon the vertical space through which it is allowed to act; a result which might, perhaps, have been anticipated. 520. Problem.--A body is projected upwards along an inclined plane with a given velocity; to find how high it will ascend, and the time of ascent. If v be the velocity at the time t, when the body has ascended through a space s, a the angle of the plane, and V the given velocity of projection, we have v2 = V2-2 g s sin a. 'When v = 0 the body will stop; hence, the distance required will be given by the equation I g sin a, For the time, we have the equation v = V--gt sin a; and the body stops when v = 0, or when g sin a. 321. Theorem.--Let A...show more

## Product details

• Paperback | 84 pages
• 189 x 246 x 4mm | 168g
• Miami Fl, United States
• English
• black & white illustrations
• 1236542827
• 9781236542823