A Collection of Problems in Illustration of the Principles of Theoretical Mechanics |
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Page 37
... Forces : the Centre of Gravity of a body is a particular case of this . Let x , y , z , denote the co - or- dinates of the point of application of any force P of the system referred to any axes , rectangular or oblique ; and let x , y ...
... Forces : the Centre of Gravity of a body is a particular case of this . Let x , y , z , denote the co - or- dinates of the point of application of any force P of the system referred to any axes , rectangular or oblique ; and let x , y ...
Page 43
... force by which it is sustained , the force being supposed to act along the plane . He then announces generally , without however supplying a corresponding extension of demonstration , that the condition of equilibrium of any three forces ...
... force by which it is sustained , the force being supposed to act along the plane . He then announces generally , without however supplying a corresponding extension of demonstration , that the condition of equilibrium of any three forces ...
Page 50
... force , when inclined to a smooth plane of the same elevation , would support the same particle . н Let e denote the least angle which the force may make with the rough plane to support the particle , P the magnitude of the force , R ...
... force , when inclined to a smooth plane of the same elevation , would support the same particle . н Let e denote the least angle which the force may make with the rough plane to support the particle , P the magnitude of the force , R ...
Page 52
... force . If denote the inclination of the force to the inclined plane , a the plane's inclination , and μ the coefficient of friction , where may have any . 0 = = a - 28 + 3π , value from tanμ to + tanμ . CHAPTER III . EQUILIBRIUM OF A ...
... force . If denote the inclination of the force to the inclined plane , a the plane's inclination , and μ the coefficient of friction , where may have any . 0 = = a - 28 + 3π , value from tanμ to + tanμ . CHAPTER III . EQUILIBRIUM OF A ...
Page 53
... forces act upon a body consisting of a system of points rigidly connected together . Take any three straight lines OA ... force of the system be resolved into two parts , the one at right angles to O'A ' , and the other parallel to it ...
... forces act upon a body consisting of a system of points rigidly connected together . Take any three straight lines OA ... force of the system be resolved into two parts , the one at right angles to O'A ' , and the other parallel to it ...
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Common terms and phrases
absolute force acted angular velocity attraction axes axis body catenary centre of force centre of gravity circle co-ordinates coefficient of friction collision cos² curve cylinder d²x denote density determine direction distance dx dy dx² elastic ellipse equal equation Euler find the centre find the position fixed point formula given velocity hence horizontal plane inclined plane integrating James Bernoulli John Bernoulli latus rectum middle point motion oscillation parabola particle perpendicular position of equilibrium pressure problem projection radius of gyration rest right angles SECT shews sin² smooth sphere square straight line string supposing surface taking moments tan² tangent tension triangle tube unit of mass varying inversely vertical plane virtual velocities Vis Viva weight zero
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