A Collection of Problems in Illustration of the Principles of Elementary Mechanics |
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Page 3
... Produce PA to T , making AT equal to AP . Through T draw the line TQ parallel to AS , cutting the curve in any point ... produced if necessary , cuts the curve in any other points Q ' , Q " , Q " , ... ; there will be other chords AQ ...
... Produce PA to T , making AT equal to AP . Through T draw the line TQ parallel to AS , cutting the curve in any point ... produced if necessary , cuts the curve in any other points Q ' , Q " , Q " , ... ; there will be other chords AQ ...
Page 4
... Produce AB , DC , to meet in T , and draw OE , OF , parallel to DC , AB , respectively . L L The angle OBE is equal to ¿ AOB + ¿ BAO , and there- fore to DOC + BAC , and therefore to DOC + BDC , or to DOC + CDO , and therefore to OCF ...
... Produce AB , DC , to meet in T , and draw OE , OF , parallel to DC , AB , respectively . L L The angle OBE is equal to ¿ AOB + ¿ BAO , and there- fore to DOC + BAC , and therefore to DOC + BDC , or to DOC + CDO , and therefore to OCF ...
Page 8
... produce the same effect as a pressure of 2P pounds applied in a given direction . The two forces P and P√3 must be at right angles to each other , their inclinations to the force 2P being 60 ° and 30 ° respec- tively . ( 16 ) Shew that ...
... produce the same effect as a pressure of 2P pounds applied in a given direction . The two forces P and P√3 must be at right angles to each other , their inclinations to the force 2P being 60 ° and 30 ° respec- tively . ( 16 ) Shew that ...
Page 12
... produce equilibrium , they must be proportional to the sides FO , OE , EF , respectively , of the triangle OEF . But P = R by sup- position : hence FO = EF , EOF = FEO , and therefore AOE , and consequently OAE , is equal to half a ...
... produce equilibrium , they must be proportional to the sides FO , OE , EF , respectively , of the triangle OEF . But P = R by sup- position : hence FO = EF , EOF = FEO , and therefore AOE , and consequently OAE , is equal to half a ...
Page 17
... produce equilibrium supposing the angle between P's direction and R's to be π , and that between Q's and R's to be π , to com- pare the magnitudes of the forces . P , Q , R , are to each other respectively as 2 , √√3 , 1 . ( 5 ) A ...
... produce equilibrium supposing the angle between P's direction and R's to be π , and that between Q's and R's to be π , to com- pare the magnitudes of the forces . P , Q , R , are to each other respectively as 2 , √√3 , 1 . ( 5 ) A ...
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attached body is projected centre of gravity chord coefficient of friction collision component cos² cylinder denote described determine distance equal forces equation feet find the position find the pressure fixed point forces act fulcrum geometry given circle given point hence highest point horizontal plane inclined plane intersection join latus rectum length lever line of quickest lowest point magnitude and direction middle point motion moveable parabola parallel particle pendulum perpendicular point of projection position of equilibrium pound weight pounds prove pully quickest descent radii radius ratio reaction respectively rest resultant right angles seconds SECT shew sides sin² sliding smooth sphere straight line string passing supposing suspended tan¹ three forces uniform rod University of Cambridge velocity of projection vertical circle vertical plane wheel
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Page 145 - OUT of childhood into manhood Now had grown my Hiawatha, Skilled in all the craft of hunters, Learned in all the lore of old men, In all youthful sports and pastimes, In all manly arts and labors. Swift of foot was Hiawatha ; He could shoot an arrow from him, And run forward with such fleetness, That the arrow fell behind him...