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Link OP rotates about O, and pin P slides in the slot attached to collar C. Determine the velocity and acceleration of collar C as a function of 0 for the following cases: (i) ^ = a; and (9 = 0, (ii) 0 = 0 and 0 = a. Analytical 32 Dynamics Problem 1/15 Problem 1/14 1/15. At the bottom A of a vertical inside loop, the magnitude of the total acceleration of the airplane is 3g. If the airspeed is 800 mph and is increasing at the rate of 20 mph per second, determine the radius of curvature of the path at A.

If the collar is Analytical 40 Dynamics X = 240 mm y = 300 mm z= 180 mm r = 200 mm Problem 1/51 released from rest at A, what are the speeds of the collar at B and C? 1/52. Prove that a force is conservative if and only if the following relations are satisfied: OF,, dy 1/53. dR, dx dz dy dF, dx OF,. dz Show that the force F_={xi + yj + zk){x^ + y^ + z^) is conservative by applying the results of Problem 1/52. Also find the potential energy function V{x^ y, z) associated with F_. 1/54. A 1/2 lb collar slides without friction on a horizontal rod which rotates about a vertical shaft.

Friction is sufficient to prevent wheel slipping. We want to find the power, Pg, delivered by the engine to the wheels. Since the wheels roll without slipping, there is no velocity at the point of contact with the road. Consequently, from Eqn. 27), F_i and F_2 do no work. Also, N_i and N_2 do no work because they are normal to any possible velocity, even if there is slipping. The kinetic and potential energies are found from Eqns. 42) as (see Fig. 1-28): T 1 _2 = -mv^ + V = mg sin 9x Ayfv-'^ 4-li- The work done by force D is U^ = f D-Edt = - jDv dt Review of Newtonian Dynamics 27 v=rco Fig.

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