Mechanics for beginners |
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Page 21
... Divide AC into a number of equal portions , each less than DE ; mark off on CE portions equal to these , and let K be the last division : then K evidently falls between D and E. Draw KG parallel to CA. Then two forces represented by AC ...
... Divide AC into a number of equal portions , each less than DE ; mark off on CE portions equal to these , and let K be the last division : then K evidently falls between D and E. Draw KG parallel to CA. Then two forces represented by AC ...
Page 31
... divides AB into segments which are inversely as the forces at A and B respectively . Let AB = a , and AD = x ; then 00 Q therefore = α - x pi Px = Q ( a - x ) , Qa therefore OC = = P + Q ' 61. To find the magnitude and direction of the ...
... divides AB into segments which are inversely as the forces at A and B respectively . Let AB = a , and AD = x ; then 00 Q therefore = α - x pi Px = Q ( a - x ) , Qa therefore OC = = P + Q ' 61. To find the magnitude and direction of the ...
Page 32
... point D such that AD Q BD P Thus D divides AB produced through B into segments which are inversely as the forces at A and B respectively . Let AB - a , and AD = x ; then 00 Q a - a- ; therefore therefore Px = Q ( x − a ) 32 RESULTANT OF.
... point D such that AD Q BD P Thus D divides AB produced through B into segments which are inversely as the forces at A and B respectively . Let AB - a , and AD = x ; then 00 Q a - a- ; therefore therefore Px = Q ( x − a ) 32 RESULTANT OF.
Page 33
... dividing the distance between them in the inverse ratio of the two forces . 63. We may find the resultant of any number of paral- lel forces by repeated application of the process of Arts . 60 and 61. First find the resultant of two of ...
... dividing the distance between them in the inverse ratio of the two forces . 63. We may find the resultant of any number of paral- lel forces by repeated application of the process of Arts . 60 and 61. First find the resultant of two of ...
Page 61
... divide it at L , so that AL may be to LB as Q is to P ; then the resultant of P at A and Q at B is P + Q parallel to them , at L. Join LC , and divide it at M , so that LM may be to MC as R is to P + Q ; then the resultant of P + Q at L ...
... divide it at L , so that AL may be to LB as Q is to P ; then the resultant of P at A and Q at B is P + Q parallel to them , at L. Join LC , and divide it at M , so that LM may be to MC as R is to P + Q ; then the resultant of P + Q at L ...
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Common terms and phrases
ABCD acceleration algebraical sum angular points axis balance beam bisects body or system centre of gravity circle coefficient of friction components conditions of equilibrium cos² couple cylinder denote described determine distance equi Euclid example feet find the centre fixed point fulcrum given heavy particles Hence horizontal plane impact inches inclined plane Law of Motion length line of action lower block magnitude and direction mechanical advantage middle point move moveable Pully P+Q+R parabola Parallelogram of Forces perpendicular point of application point of projection position Power preceding Article pressure proposition radius ratio Resolved displacement respectively rest right angles rigid body Screw shew single resultant smooth string which passes system of forces System of Pullies Take moments round tension three forces tion triangle turn round uniform vanishes velocity vertical weight Wheel and Axle
Popular passages
Page 327 - The squares of the periodic times are proportional to the cubes of the major axes of the orbits.
Page 295 - Change of motion is proportional to the impressed force, and takes place in the direction of the straight line in which the force acts.
Page 295 - 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.
Page 10 - ... is represented in magnitude and direction by that diagonal of the parallelogram which passes through the particle.
Page 237 - ... point, then the resultant velocity will be represented in magnitude and direction by the diagonal, drawn from that point, of the parallelogram constructed on the two straight lines as adjacent sides.
Page 134 - This proportion teaches us that, when in equilibrium, the power is to the weight as the height of the plane is to its length.
Page 96 - The straight lines which join the middle points of the opposite sides of any quadrilateral bisect each other...
Page 16 - If three forces acting on a particle keep it in equilibrium, each force is proportional to the sine of the angle between the directions of the other two.
Page 13 - Then it is obvious that the particle will be in equilibrium; for there is no reason why it should move in one direction rather than in another.
Page 290 - A ball is projected in a given direction within a fixed horizontal hoop, so as to go on rebounding from the surface of the hoop ; find the limit to which the velocity will approach, and shew that it attains this limit in a finite time, e being less than 1.