| 1867
...<rei<r<£x9(ia, EXAMINATION FOE THE MA DEGREE. SATURDAY, April 17, 1875. NATURAL PHILOSOPHY. 1. Prove that **if three forces are in equilibrium each is proportional to the sine of the** angle contained by the other two. What additional condition must be fulfilled in order that the converse... | |
| William John Macquorn Rankine, Edward Fisher Bamber - 1873 - 312 Seiten
...other, or in other words, that three forces in the same plane balance each other at one point, when **each is proportional to the sine of the angle between the other two.** 211. Polygon of Forces. — If a number of forces acting through the same point be represented by lines... | |
| William John Macquorn Rankine, Edward Fisher Bamber - 1873 - 312 Seiten
...oiher, or in other words, that three forces in the same plane balance each other at one point, when **each is proportional to the sine of the angle between the other two.** 211. Polygon of Forces. — If a number of forces acting through the same point be represented by lines... | |
| Julius George Medley - 1873 - 1184 Seiten
...Load compresses both bars; and since the three stresses (-7- -f- w' ),<,', A, are in equilibrio at C', **each is proportional to the sine of the angle between the other two,** í. в., ^L + wj ; t,' : А„ = sin A'C'C" : sin C"C'M- : sin A'C'M" = sin í : 1 : cos » Л í,'... | |
| James Russell Soley - 1880 - 335 Seiten
...State the parallelogram of forces, and deduce from it that, if three forces acting on a particle be **in equilibrium, each is proportional to the sine of the angle between the other two.** A small ring of given weight rests on the arc of a smooth circular hoop which is fixed in a vertical... | |
| United States. Congress. Senate - 1880
...State the parallelogram of forces, and deduce from it that, if three forces acting on a particle be **in equilibrium, each is proportional to the sine of the angle between the other two.** A small ring of given weight rest» on the arc of a smooth circular hoop which is filed in a vertical... | |
| Adolphe Ganot - 1886 - 1031 Seiten
...the sines of the angles are equal to the sines of their supplements, we at once conclude that •when **three forces are in equilibrium, each is proportional to the sine of** t/te angle between the directions of the other two. •^ 36. Momenta at Forces. — Let P (fig. 12)... | |
| John Greaves - 1888 - 274 Seiten
...parallelogram of forces in another form. -J " \ Prop. If three forces acting on a particle, keep it in ". I **equilibrium, each is proportional to the sine of the angle * between the other two.** Let OA, OB, OC represent three forces P, Q, R which, acting on a particle, keep it in equilibrium.... | |
| Thomas Wallace Wright - 1890 - 254 Seiten
...^/ysin (180° - y), or ./P/sin a = F,/sia ft = F,/sin y; that is, when three forces acting on a particle **are in equilibrium, each is proportional to the sine of the angle between the** directions of the other two forces. Illustration. — Take a piece of board, and drive in three smooth... | |
| Sidney Luxton Loney - 1891
...together are less than the third. 40. Lami's Theorem. If three forces acting on a particle keep it **in equilibrium, each is proportional to the sine of the angle between the other two.** Taking Fig., Art. 38, let the forces P, Q, R be in equilibrium. As before, measure off lengths OL,... | |
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