Elements of Mechanics: For the Use of Colleges, Academies, and High SchoolsA.S. Barnes & Burr, 1859 - 338 pages |
From inside the book
Results 1-5 of 49
Page 31
... SOLUTION . We have , X = 9 , and Y = 12 ; . R = √81 +144 = 15 . 9 Also , cos a = = .6 ; a = 53 ° 7 ' 32. " 15 That is , the resultant pressure is 15 lbs . , and it makes an angle of 53 ° 7 ′ 32 " with the direction of the first force ...
... SOLUTION . We have , X = 9 , and Y = 12 ; . R = √81 +144 = 15 . 9 Also , cos a = = .6 ; a = 53 ° 7 ' 32. " 15 That is , the resultant pressure is 15 lbs . , and it makes an angle of 53 ° 7 ′ 32 " with the direction of the first force ...
Page 32
... SOLUTION . X = We have , 3X = 4Y , or X = Y , and R = 20 ; Hence , 2 2 20 = √X2 + 2X2 = { X ; X = 12 , and Y = 16 . 3. A boat fastened by a rope to a point on the shore , is urged by the wind perpendicular to the current , with a force ...
... SOLUTION . X = We have , 3X = 4Y , or X = Y , and R = 20 ; Hence , 2 2 20 = √X2 + 2X2 = { X ; X = 12 , and Y = 16 . 3. A boat fastened by a rope to a point on the shore , is urged by the wind perpendicular to the current , with a force ...
Page 33
... intensity and direction of the resultant of three forces at right angles to each other , having the in- tensities 4 , 5 , and 6 pounds , respectively . SOLUTION . We have , X = 4 , Y 2 * COMPOSITION AND RESOLUTION OF FORCES . 33.
... intensity and direction of the resultant of three forces at right angles to each other , having the in- tensities 4 , 5 , and 6 pounds , respectively . SOLUTION . We have , X = 4 , Y 2 * COMPOSITION AND RESOLUTION OF FORCES . 33.
Page 34
... SOLUTION . We have Hence , 60 = Y = 3X , Z = 2X , and R = 60 ; ' X2 + 2X2 + 4X2 = X√29 = 2.6925 X .. X = 22.284 . The components are , therefore , 22.284 lbs . , 33.426 lbs . , and 44.568 lbs . Projection of Forces . 32. If planes be ...
... SOLUTION . We have Hence , 60 = Y = 3X , Z = 2X , and R = 60 ; ' X2 + 2X2 + 4X2 = X√29 = 2.6925 X .. X = 22.284 . The components are , therefore , 22.284 lbs . , 33.426 lbs . , and 44.568 lbs . Projection of Forces . 32. If planes be ...
Page 35
... angles equal to 15 ° , 30 ° , and 45 ° , respectively . Required the intensity and direction of the resultant . SOLUTION . We have , X = 50 cos 15 COMPOSITION AND RESOLUTION OF FORCES . 35 . Composition of a Group of Forces in a Plane.
... angles equal to 15 ° , 30 ° , and 45 ° , respectively . Required the intensity and direction of the resultant . SOLUTION . We have , X = 50 cos 15 COMPOSITION AND RESOLUTION OF FORCES . 35 . Composition of a Group of Forces in a Plane.
Contents
64 | |
71 | |
80 | |
94 | |
101 | |
105 | |
112 | |
118 | |
125 | |
133 | |
140 | |
146 | |
153 | |
161 | |
165 | |
175 | |
182 | |
238 | |
249 | |
255 | |
261 | |
268 | |
274 | |
280 | |
286 | |
290 | |
296 | |
304 | |
310 | |
318 | |
324 | |
331 | |
337 | |
Other editions - View all
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...