Elements of Mechanics: For the Use of Colleges, Academies, and High SchoolsA.S. Barnes & Burr, 1859 - 338 pages |
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Page 37
... substituting ( 6 ) , and reducing by the relation 1 , we have , √P2 + P'2 + 2PP ' cos a ' ( 7. ) The angle a ' is the angle included between the given forces . Hence , The resultant of any two forces , applied at the same point , is ...
... substituting ( 6 ) , and reducing by the relation 1 , we have , √P2 + P'2 + 2PP ' cos a ' ( 7. ) The angle a ' is the angle included between the given forces . Hence , The resultant of any two forces , applied at the same point , is ...
Page 41
... Substituting in the preceding equation , and reducing , we have , RrQqPp . When the point C falls within the angle POR , & α becomes negative , and the equation just deduced becomes Rr = Qq - Pp . Hence , we conclude in all cases , that ...
... Substituting in the preceding equation , and reducing , we have , RrQqPp . When the point C falls within the angle POR , & α becomes negative , and the equation just deduced becomes Rr = Qq - Pp . Hence , we conclude in all cases , that ...
Page 44
... Substituting these in the preceding equation , and reducing , we have , Ror Pop + Qoq . Hence , the virtual moment of the resultant of two forces , is equal to the algebraic sum of the virtual moments of the two forces taken separately ...
... Substituting these in the preceding equation , and reducing , we have , Ror Pop + Qoq . Hence , the virtual moment of the resultant of two forces , is equal to the algebraic sum of the virtual moments of the two forces taken separately ...
Page 48
... Substituting in the preceding proportions P + Q , P — Q , SN + SM , and SN - SM , their values , we have , P : QR :: SN : SM : MN . That is , of two parallel forces and their resultant , each is proportional to the distance between the ...
... Substituting in the preceding proportions P + Q , P — Q , SN + SM , and SN - SM , their values , we have , P : QR :: SN : SM : MN . That is , of two parallel forces and their resultant , each is proportional to the distance between the ...
Page 52
... lever arms of the components , x , x ' , x ' , & c .; and from the principle of moments ( Art . 36 ) , Reosyx , Pcosy x + P'cosy x ' + & c . = Striking out the common factor cos y , and substituting 52 MECHANICS . Centre of Parallel Forces.
... lever arms of the components , x , x ' , x ' , & c .; and from the principle of moments ( Art . 36 ) , Reosyx , Pcosy x + P'cosy x ' + & c . = Striking out the common factor cos y , and substituting 52 MECHANICS . Centre of Parallel Forces.
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Common terms and phrases
A. S. BARNES algebraic sum angular velocity atmosphere axes axle body called centre of gravity centrifugal force cistern components cord cubic cubic foot curve cylinder denote the angle distance elementary entire equal Equation equilibrium exerted feet fluid force applied force of gravity forces acting friction fulcrum Hence horizontal hydrometer inches inclined plane inertia instrument lever arm liquid machine mass mercury moment of inertia moments motion orifice parallel forces parallelogram parallelogram of forces particles passing Pcosa pendulum perpendicular pipe piston point of application polygon position power and resistance pressure principle principle of moments pulley pump quantity radius radius of gyration represent reservoir respect resultant right angles rope rotation Schools screw SOLUTION space specific gravity square steam Substituting suppose temperature tension tion triangle tube unit upper surface vertex vertical vessel vibration volume weight wheel whence
Popular passages
Page 182 - ... plus the product of the area and the square of the distance between the axes.
Page 223 - This electromotive force may be resolved into two components, one parallel and the other perpendicular to I, as shown, for example, in Fig.
Page 114 - The power is to the weight, as the radius of the pulley is to the chord of the arc enveloped by the rope.
Page 39 - 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.
Page 7 - BOURDON'S ALGEBRA 1 50 KEY TO DAVIES' BOURDON'S ALGEBRA 1 50 DAVIES' LEGENDRE'S GKOMETRY 1 50 DAVIES' ELEMENTS OF SURVEYING 1 50 DAVIES' ANALYTICAL GEOMETRY 1 25 DAVIES' DIFFERENTIAL AND INTEGRAL CALCULUS 1 25 DAVIES' DESCRIPTIVE GEOMETRY 2 00 DAVIES...
Page 42 - Hence, the moment of the resultant of two forces is equal to the algebraic sum of the moments of the forces taken separately. 53. Forces Acting at Different Points. Parallel Forces.— We have thus far considered forces acting upon a single particle, or upon one point of a body. If, how- Fia 33...
Page 180 - ... must be measured on a line at right angles to the direction of the force. Moment of Inertia. The moment of inertia of a body, with respect to an axis, is the sum of the products obtained by multiplying the mass of each elementary particle by the square of its distance from the axis; hence, the moment of inertia of the same body varies according to the position of the axis.
Page 5 - ... feet. Thus it appears, that it requires a force to lift the piston exactly equal to the weight of a column of water, whose base is equal to the section of the piston, and whose height...
Page 8 - JOHN A.* PORTER, AM. MD, Professor of Agricultural and Organic Chemistry in Yale College. Price $1.00. These works have been prepared expressly for Public and Union Schools, Academies, and Seminaries, where an extensive course of study on this subject and expensive apparatus was not desired, or could not be afforded. A fair, practical knowledge of Chemistry is exceedingly desirable, and almost a necessity, at tho present day, but it has been...