An Elementary Treatise On Mechanics Vol 2

Author : Richard Potter
Publisher : Rarebooksclub.com
ISBN 13 : 9781230006505
Total Pages : 38 pages
Book Rating : 4.0/5 (65 download)

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Download or read book An Elementary Treatise on Mechanics for the Use of Junior University Students written by Richard Potter and published by Rarebooksclub.com. This book was released on 2013-09 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 1859 edition. Excerpt: ...will be the same, =m say; and the number of cords at the lower block will be 2m, and then 2m 2m If the weight of the pullies be counterpoised or neglected, we have W 48. Prop. To find the relation of the power to the weight in a combination of pullies when the cords are parallel, and each attached to the weight. This is called the third system of pullies. In this system the uppermost pulley is fixed, and its weight is supported by the beam to which they are attached. Let wx be the weight of the pulley ax; w%, ws those of the pullies a2, a3 respectively. Let ti3 t2, t9, t4 be the tensions in the cords respectively, and t, = P, t2=z2tl + w1 = 2P + w1) t3=22 + wq-22P + 2w1 + wz, t4 = 2t3 + w3== 23P + 22wl + 2w2 + w3, and W=tx + t2 + t3 + t4 = P(l+2 + 22 + 23) + w1(l+2 + 22) + w2(l + 2)+w3 = p (24 _ 1) + w 1 (23-1) + M, a (22-1) H-t8(2-l). If the system contains n moveable pullies, we shall have similarly, TV= P(2n+1-1) + wx 2n-1) + w22n1-1) + &c + wn2-1). If the n pullies were of the same weight wv we should have W=P(2n+l-l)+wl2n + 2n-l+2n-2 + &c.... +2)-nwl = P(2+1-l) + wl(2+1-2--rc) = (P + Wl) (2n+l-l)-n + l)wv In this system the weights of the pullies assist the power. If they are balanced independently, or neglected, we have W J=(2+'-l). ON THE INCLINED PLANE. When a particle or body is in contact with any hard surface, plane or curved, and the forces press it against the surface, the normal reaction of the surface is one of the forces concurring to produce equilibrium, and must be considered with the other forces. The inclined plane, as a mechanical power, is supposed perfectly hard and smooth (unless the friction is considered); and having some angle of elevation above the horizontal plane, has a heavy particle...