A Treatise on DynamicsBell and Company, 1893 - 448 páginas |
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Página 57
... string and pulled apart ; potential energy is thus stored up , and if the balls be let go , kinetic energy is acquired which is the exact equivalent of the loss of potential energy due to the contraction of the string . 52. The ...
... string and pulled apart ; potential energy is thus stored up , and if the balls be let go , kinetic energy is acquired which is the exact equivalent of the loss of potential energy due to the contraction of the string . 52. The ...
Página 62
... string passing over a smooth fixed pulley . If m , m ' be the masses , T the tension of the string and x the distance of m from the pulley , mx = mg — T , - and similarly a being the distance of the other weight , - x - — m'ï = m'g — T ...
... string passing over a smooth fixed pulley . If m , m ' be the masses , T the tension of the string and x the distance of m from the pulley , mx = mg — T , - and similarly a being the distance of the other weight , - x - — m'ï = m'g — T ...
Página 68
... string . If x be the length at the time t , and T the tension , the equation of motion is or whence α mä = mg — T = mg −λa , by Hooke's Law , - ä + X - α - λ ma mag λ a ( mag XC -α = λ = A cos √ λ λ t + B sin ma ma Suppose that ...
... string . If x be the length at the time t , and T the tension , the equation of motion is or whence α mä = mg — T = mg −λa , by Hooke's Law , - ä + X - α - λ ma mag λ a ( mag XC -α = λ = A cos √ λ λ t + B sin ma ma Suppose that ...
Página 74
... string is given by the equations m ( u ' — u ) = — Q , μu ' = Q , the effect of the impulse on each body being change of momentum . Subsequently , if t be the time which elapses before the lower string becomes tightened , ut — 1gt2 = u ...
... string is given by the equations m ( u ' — u ) = — Q , μu ' = Q , the effect of the impulse on each body being change of momentum . Subsequently , if t be the time which elapses before the lower string becomes tightened , ut — 1gt2 = u ...
Página 76
... string , and we thus have dv μου = Τ ' -ημα - μυς , dx dv μx v = dx = gμx — T ' , - and adding these equations we obtain the same result as before . 77. Two coils of heavy uniform chains are fastened to 76 RECTILINEAR MOTION .
... string , and we thus have dv μου = Τ ' -ημα - μυς , dx dv μx v = dx = gμx — T ' , - and adding these equations we obtain the same result as before . 77. Two coils of heavy uniform chains are fastened to 76 RECTILINEAR MOTION .
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Términos y frases comunes
acting forces action angular momentum axes ball body centre of force centre of gravity chain circle circular component constant coordinates cos² curve cycloid described determine the motion diameter direction of motion disc distance ds ds Edition elastic string ellipse equal equations of motion equilibrium Fcap fixed point given h₁ heavy particle Hence hodograph horizontal plane hyperbola impulses inclination initial instant kinetic energy latus rectum mass moment of inertia momenta natural length normal obtain orbit parabola particle moves path perpendicular point moves position prove radius of curvature radius vector relative revolve ring rotation shew sin² smooth horizontal plane sphere straight line surface Taking tangent tension time-flux tube uniform angular velocity uniformly vertex vertical plane weight
Pasajes populares
Página 48 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.