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" When three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two. "
Mechanics for junior students - Σελίδα 23
των William James Browne - 1883 - 200 σελίδες
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Cambridge Senate-house Problems and Riders for the Year 1860: With Solutions

Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...and, assuming its truth for the magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium,...proportional to the sine of the angle between the other two. Two equal particles, each attracting with a force varying directly as the distance, are situated at...

Cambridge Senate-house Problems and Riders for the Year 1860: With Solutions

Henry William Watson, Edward John Routh - 1860 - 240 σελίδες
...and, assuming its truth for the magnitude, prove it also for the direction, of the resultant. 2. When three forces acting at a point are in equilibrium,...proportional to the sine of the angle between the other two. Two equal particles, each attracting with a force varying directly as the distance, are situated at...

An elementary treatise on Mechanics

Stephen Parkinson - 1863 - 408 σελίδες
...the parallelogram of forces we can easily deduce the following theorem first stated by Lami, in 1687. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle contained between the directions of the remaining two. For referring to the fig. of Art. (20),...

An Elementary Treatise on Mechanics for the Use of the Junior Classes at the ...

Stephen Parkinson - 1863 - 396 σελίδες
...their directions are not parallel : — (i) Their lines of action must meet in a point, Art. (22). (ii) Each force is proportional to the sine of the angle between the other two, the direction of each force lying without the angle formed by the other two, Art. (23). For this latter...

Mechanics required for the Additional Subjects for Honours at the Previous ...

James McDowell - 1867 - 120 σελίδες
...(Euc. I. 47) that is, K2 therefore B = </(P* + <?"). QED *24. If three forces acting at a point be in equilibrium, each force is proportional to the sine of the angle between the other two, (Fig. 1. Art. 16.) Let the three forces P, Q, R, acting at 0, be in equilibrium, and be represented...

Mechanics for Beginners: With Numerous Examples

Isaac Todhunter - 1867 - 372 σελίδες
...of a triangle perpendicular to the lines of action. 38. If three forces acting on a particle keep it in equilibrium, each force is proportional to the sine of the angle between the directions of the other two. Let forces P, Q, R acting on a particle at 0 keep it in equilibrium. Then,...

Mechanics for beginners

Isaac Todhunter - 1867 - 368 σελίδες
...of a triangle perpendicular to the lines of action. 38. If three forces acting on a particle keep it in equilibrium, each force is proportional to the sine of the angle between the directions of the other two. Let forces P, Q, R acting on a particle at 0 keep it in equilibrium. Then,...

A Treatise on Elementary Statics, Τόμος 12

James Hamblin Smith - 1868 - 102 σελίδες
...similar triangles. Hence and and MN : NO :: AB :: P NO : OH:: BD OM : MN:: DA :: R BD Q DA S, AB P. xxii. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle contained between the directions of the other two. Let P, Q, R be the three forces. a, /8, y...

Chambers's Encyclopædia: A Dictionary of Universal Knowledge for ..., Τόμος 9

Ephraim Chambers - 1870 - 872 σελίδες
...substituting the sines of the supplementary angles) : : ein. QAR' : sin. PAH' : sin. PAQ ; that is, each force is proportional to the sine of the angle between the directions of the other tw o. TRIA'NGULAR NUMBERS. See FIOCRAT* NUMBERS. TRIANGULATION is the operation...

Elementary Introduction to Practical Mechanics: Illustrated by Numerous Examples

bart John Francis Twisden (Sir) - 1870 - 394 σελίδες
...: K : : sin RAP: sin p A Q. These proportions are sometimes expressed by the rule, <If three forces are in equilibrium, each force is proportional to the sine of the angle contained by the other two.(2) Employing the same figure, we have, by a wellknown theorem in...




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