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. 1917 Excerpt: ...and the vertical component of P. The force of friction, F, is then n (W--P sin 0). The horizontal component of P equals F. Hence n (W-P sin 0) = P cos 0, or = cos0+/isin0. (2) flW Since n and W are constants, -p-is a maximum when and only when P is a minimum. Hence to find the minimum value of P uW we may find the ...
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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. 1917 Excerpt: ...and the vertical component of P. The force of friction, F, is then n (W--P sin 0). The horizontal component of P equals F. Hence n (W-P sin 0) = P cos 0, or = cos0+/isin0. (2) flW Since n and W are constants, -p-is a maximum when and only when P is a minimum. Hence to find the minimum value of P uW we may find the maximum value of-p-and multiply its reciprocal by p.W where a is an angle in the first quadrant whose tangent is ft, the coefficient of friction. Therefore, when 6 is acute and equal U.W to tan-1 ft, P is a minimum and equal to. VI + M2 Illustration 2. A weight, W, Fig. 64, rests upon the inclined plane AB. Find 6 so that P, the force which will just cause W to move up the plane, shall be a minimum. The normal pressure, N, between the weight and the plane AB is equal to W cos P--P sin 6. Then F, the force of friction, is equal to n (W cos / 3-P sin 6), . where n is the coefficient of friction. We have then F = ii(WcosP-Psin0). Since the force of friction must balance the components of P and W parallel to the plane AB, we have n(W cos /3-P sin 6) = (P cos 6-W sin /3). Hence JFGucos/3 +sin/3) or TFQu cos/3 +sing), p = VI + /x2 cos (9-a ). (3) where a is the acute angle whose tangent is /x. Thus, the lefthand side of (3) is a maximum, and P a minimum, when 6 is acute and equal to tan-1 p. T, .... D... TPQucosfl + sin/?) The minimum value of P is then. vTT72 Exercise In Fig. 64, find the minimum force, P, and the angle between its line of action and AB, which will just prevent the weight W from sliding down the plane. 91. The Function mx y/a?--x2. Frequently problems in maxima and minima lead to functions of the form mx /o2--z2. The curve for y = mx Va2--x2 (1) can be obtained by shearing the circle y= s/a1--x2 in the line y =...
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Add this copy of Calculus to cart. $21.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Calculus to cart. $21.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Calculus to cart. $31.73, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Calculus to cart. $31.73, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Calculus to cart. $34.12, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of Calculus to cart. $34.12, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
