97K/s llO &e 7:23۱۰۳۹ من ۱۰۶۰PROBLEMS77will jump outward. We expect the bifurcation point, the point wherethe equationsignificance. As we shall see in Example 3.10, w= Vg/l is the oscilla-tion frequency, in radians per second, of a simple pendulum of length I.If the rotation frequency is less than this value, the pendulum can hangvertically. (It could also swing back and forth, executing pendulum mo-tion.) However, for a rotation frequency higher than the pendulum fre-quency, the pendulum will fly outward, unless it is precisely vertical.Can you see why this is so?motion suddenly has two solutions, has some specialThe moral of this example is that it is important to check that a mathe-matical solution makes good physical sense.ProblemsFor problems marked *, refer so page 520 for a hint, clue, or answer.2.1 Time-dependent force*A S-kg mass moves under the influence of a force F (4ri-3j)N,where t is the time in seconds (1 N = 1 newton). It starts at restfrom the origin at t = 0. Find: (a) its velocity; (b) its position; and(c) rxv, for any later time.22 Two blocks and stringThe two blocks M and M2 shown in the sketch are connected bya string of negligible mass. If the system is released from rest, findhow far block M, slides in time t. Neglect friction.M.2.3 Two blocks on tableTwo blocks m, and m; are in contact on a horizontal table. A hor-izontal force is applied to one of the blocks, as shown in the draw-ing. If m, = 2 kg, m, = 1 kg, and F = 3N, find the force of contactbetween the two blocks.2.4 Circling particle and forceTwo particles of mass m and M undergo uniform circular motionabout each other at a separation R under the influence of an attrac-tive constant force F. The angular velocity is w radians per second.Show that R= (F/)(1/m+ 1/M).2.5 Concrete mixerIn a concrete mixer, cement, gravel, and water are mixed by tum-bling action in a slowly rotating drum. If the drum spins too fastthe ingredients stick to the drum wall instead of mixing.Assume that the drum of a mixer has radius R = 0.5 m and thatit is mounted with its axle horizontal. What is the fastest the drumcan rotate without the ingredients sticking to the wall all the time?Assume g=9.8 m/s.طفولیه B2:38, äclull 21.02.26

Answered: Image /qna-images/answer/b9276329-3f26-46e4-a2ac-1f4e3fc5da57.jpg

21 Time-dependent force AS-kg mass moves under the influence of a force F (4i-3¢])N, where r is the time in seconds (1 N = I newton). It starts at rest from the origin at t=0. Find: (a) its velocity; (b) its position; and (c)rxv, for any later time.

21 Time-dependent force AS-kg mass moves under the influence of a force F (4i-3¢])N, where r is the time in seconds (1 N = I newton). It starts at rest from the origin at t=0. Find: (a) its velocity; (b) its position; and (c)rxv, for any later time.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.40P: An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for...

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