. Contributions. — a. Case (b): c and c^ are rough, the coefficients of friction being ^iand ;u-^. As before, call T the tension in the rod, V and V^ the velocitiesof m and m^\ the equations of motion of the two particles are then mj = - /i I -- - Tj, J = - ft ay-Q - ^^ [, the upper or lower sign being taken according as p ^ «; i. e. accordingas the velocities of the two particles have the same or opposite relation becomes + ii, I co\q - a) + — I + (1 - ^j ,u 09^ - ,„ i = c^ d7 • l!v l* i: l-iKi i> ;>i:. If our conditions are conipiitible it must be possible to iletermine Tso a
. Contributions. — a. Case (b): c and c^ are rough, the coefficients of friction being ^iand ;u-^. As before, call T the tension in the rod, V and V^ the velocitiesof m and m^\ the equations of motion of the two particles are then mj = - /i I -- - Tj, J = - ft ay-Q - ^^ [, the upper or lower sign being taken according as p ^ «; i. e. accordingas the velocities of the two particles have the same or opposite relation becomes + ii, I co\q - a) + — I + (1 - ^j ,u 09^ - ,„ i = c^ d7 • l!v l* i: l-iKi i> ;>i:. If our conditions are conipiitible it must be possible to iletermine Tso as to satisfy this equation. To study the meaning of this condition put y. T -\- co-«,(_9 and suppose first that () > first equation is satisfietlby the points on the ))rokenline A^B^C^ and the secondby the points on A^R,(\, j,(Fig. 6) and the equationwhich T must satisfy can be-written Figs. 6, 1, 8 correspond to^f^A >(l_«)f respectivelv. In 6 we have two solutions,one, or none according as. In 7 there are one, an infinitenumber, or no solutions accor- A Fig. 7. .4, 1- C, ding as a^a , I -< ^^^ ^iin 8 there are two, one, ornone according as ds < Suppose next that p < «:the equation in T becomes Vi - y-2 dg G,
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Keywords: ., bookcentury1900, bookdecade1910, bookidcontribution, bookyear1915
