Analytical mechanics for students of physics and engineering . EQUILIBRIUM OF A PARTICLE 21 l l i I | [ i.

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RM2AKCGB6–Analytical mechanics for students of physics and engineering . General LibraryUniversity of California Berkeley $s GENERAL LIBRARY U.C. BERKELEY. SS JS THE UNIVERSITY OF CALIFORNIA LIBRARY

RM2AKGC9W–Analytical mechanics for students of physics and engineering . - A, = 0, sy - Xt + Fz - w = o, 2G0= F2l cos a + Nil >in a cos a = 0. lere a is the required angle. We have further -ft F, A. 44 ANALYTICAL MECHANICS Solving these we get Fx = r-£-t w, 1 + M.

RM2AKCT1H–Analytical mechanics for students of physics and engineering . to determine the velocity of projectile-.The target, which is suspended from a horizontal axis, isgiven an angular displacement when it receives the projec-tile. Considering the target and the bullet which is projectedinto it as an isolated system we apply the principles of theconservation of energy and of the conservation of angularmomentum. Just before the bullet hitsthe target the angular momentum ofthe system about the axis is that dueto the velocity of the bullet and equals / 7, where / is the moment of inertiab of the bullet

RM2AKG1XD–Analytical mechanics for students of physics and engineering . d of a vector describes a circle at a constant rate. If theorigin is outside the circle find the velocity along and at right an| the vector. Discuss the values for interesting special positions. 10. In the preceding problem derive an expression for the angularvelocity of the vector and discuss it. ACCELERATION 86. Acceleration.- -When the velocity of a particle changes it is said to have an acceleration. The change may lie inthe magnitude of the velocity, in the direction, or in both;further it maybe positive or negative. Therefore

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RM2AKFJ0C–Analytical mechanics for students of physics and engineering . of the string, the reaction at the joint, and the reaction of the table.Suppose a slighl displacement to be given to the system by pressing down-ward at the joint. The work done by the force which produced the dis-placement equals the sum of the work done by the other forces which actupon the rods during the displace-ment. Bui since both the force ap-plied and the displacement producedare very small their product is negli-gible. Therefore the sum of the workdone by all the other forces is zero. The reactions at the ends of therod-

RM2AKG5HM–Analytical mechanics for students of physics and engineering . Thus the equation represents, approximately, the curve in the neighbor] d of the lowest point. It will be observed thai (14) is theequation of a parabola. This result would l>r expectedsince the curve is practically straight in the neighborhoodof 0 and consequently the horizontal distribution of massis very nearly constant, which is the important feature ofthe Suspension Bridge problem. The nature of those parts of the curve which are removedfrom the lowest point may be studied by supposing x to be large. Then since ca becomes

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Analytical mechanics for students of physics and engineering . EQUILIBRIUM OF A PARTICLE 21 l l i I | [ i.

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