An Elementary Treatise On Theoretical Mechanics
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Theoretical Mechanics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Theoretical Mechanics
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Fig. 128 If the velocities of A before impact make angles a, a' with AB as marked in the figure, the tangential velocities of A before and after impact are ^^^^^^ -^tan«', so that, since the tangential velocities remain unaltered, we must have . / .
V tana'= — w tana; while similarly, from the motion of B, v' tan 13' — — u' tan /S.
Thus equations (88) and (89) become * , mu + m'u' — em'(u — u') cot a'= ; — -^^ cot a, (m + m')u , „, mu + m'u' + em(u — u') , „ cot /3' = ; -^, '- cot ^, (m + m) u'... giving a', /3' in terms of the initial motion.
248 MOTION OF SYSTEMS OF PAETICLES If, as in the game of billiards, the spheres are of equal mass and the second sphere is originally at rest, we take m — ml , u' = 0, and ■°^*^^^^ cot a' = - ^ ( 1 - e) cot a, /3' = 0.
Thus B starts into motion along the line of centers, as it obviously must since the forces which set it in motion act along this line.
Since e is always less than unity and a is necessarily acute, cot a' must be negative, so that a' wiU be obtuse.
What to read after An Elementary Treatise On Theoretical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Jeans, Sir James Hopwood, 1877-1946 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Fig. 128 If the velocities of A before impact make angles a, a' with AB as marked in the figure, the tangential velocities of A before and after impact are ^^^^^^ -^tan«', so that, since the tangential velocities remain unaltered, we must have . / .
V tana'= — w tana; while similarly, from the motion of B, v' tan 13' — — u' tan /S.
Thus equations (88) and (89) become * , mu + m'u' — em'(u — u') cot a'= ; — -^^ cot a, (m + m')u , „, mu + m'u' + em(u — u') , „ cot /3' = ; -^, '- cot ^, (m + m) u'... giving a', /3' in terms of the initial motion.
248 MOTION OF SYSTEMS OF PAETICLES If, as in the game of billiards, the spheres are of equal mass and the second sphere is originally at rest, we take m — ml , u' = 0, and ■°^*^^^^ cot a' = - ^ ( 1 - e) cot a, /3' = 0.
Thus B starts into motion along the line of centers, as it obviously must since the forces which set it in motion act along this line.
Since e is always less than unity and a is necessarily acute, cot a' must be negative, so that a' wiU be obtuse.
What to read after An Elementary Treatise On Theoretical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by Jeans, Sir James Hopwood, 1877-1946 to read onlineMoreLess
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