Elements of Mechanics: For the Use of Colleges, Academies, and High SchoolsA.S. Barnes & Burr, 1859 - 338 pages |
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Page 38
... equal to Q. From the triangle ORP we have , in accor- dance with the principles of trigo- nometry , Fig . 13 . R P : QR :: sin ORP : sin ROP : sin OPR . ( 8. ) If we apply a force R ' equal and directly opposed to R , the forces P , Q ...
... equal to Q. From the triangle ORP we have , in accor- dance with the principles of trigo- nometry , Fig . 13 . R P : QR :: sin ORP : sin ROP : sin OPR . ( 8. ) If we apply a force R ' equal and directly opposed to R , the forces P , Q ...
Page 39
... equal in intensity to 24 and 30 , respectively , and the angle between them is 105 ° . What is the intensity of their resultant ? R = √242 + 302 + 2 × 24 × 30 cos 105 ° = 33.21 . 2. Two forces , P and Q , whose intensities are respec ...
... equal in intensity to 24 and 30 , respectively , and the angle between them is 105 ° . What is the intensity of their resultant ? R = √242 + 302 + 2 × 24 × 30 cos 105 ° = 33.21 . 2. Two forces , P and Q , whose intensities are respec ...
Page 42
... equal to the algebraic sum of the moments of the forces taken separately . If we regard the force as the resultant of two others , and one of these in turn , as the resultant of two others , and so on , the principle may be extended to ...
... equal to the algebraic sum of the moments of the forces taken separately . If we regard the force as the resultant of two others , and one of these in turn , as the resultant of two others , and so on , the principle may be extended to ...
Page 43
... equal to the moment of the projection of the force upon a plane at right - angles to the axis , taken with respect to the point in which this axis pierces the plane as a centre of moments . If there are any number of forces situated in ...
... equal to the moment of the projection of the force upon a plane at right - angles to the axis , taken with respect to the point in which this axis pierces the plane as a centre of moments . If there are any number of forces situated in ...
Page 45
... equal to 0 ; con- versely , if the algebraic sum of the virtual moments of the forces is equal to 0 , the resultant is also equal to 0 , and the forces are in equilibrium . This principle , and the preceding one , are much used in ...
... equal to 0 ; con- versely , if the algebraic sum of the virtual moments of the forces is equal to 0 , the resultant is also equal to 0 , and the forces are in equilibrium . This principle , and the preceding one , are much used in ...
Contents
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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...