The crank OA rotates in the vertical plane with a constant clockwise angular velocity wo of 2.8 rad/s. For the position where OA is horizontal, calculate the force under the light roller B of the 18.1-kg slender bar AB. 1.02 m B 0.51 m 1.30 m

a.ag2x = -15,2 & ag2y = -32,6 b.ag2x = -9,3 & ag2y = -34,8 c.aG2x = -20,7 & ag2y = -29,5 d.ag2x = -3,1 & ag2y = -35,9 e.aG2x = -32,6 & ac2y = -15,2 f.ag2x = -35,9 & ag2y = -3,1 g.aG2x = -29,5 & aG2y = -20,7 h.ag2x = -34,8 & aczy = -9,3 i.aG2x = -25,5 & agzy = -25,5 j.a62x = 3,1 & ag2y = -35,9

Problem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a)…

Consider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground.   What is the potential energy of the system in terms of x?

Dynamics

2) In figure, two blocks are connected by a massless string over a pulley of radius, 2R, and rotational inertia, I. When this system is released at rest, the blocks (masses: m₁ = m and m₂ = 3m) are moving with a constant acceleration. (The friction constant between my and the surface is equal to μ.) a) Draw the free body diagram and write the Newton's equations for both masses and pulley. b) Find the angular velocity of the pulley in 5 second. m₁-m m₂=3m

Consider the model for a 2D single link robot arm shown below. The arm is pinned at the bottom as shown and there is a torsional friction of magnitude bỎ at the pin. In addition, a control torque, T, is applied at the pin. (i) g Ꮎ m, L Show that the equation of motion may be written as: m[² 3 Ô +bỏ + mgL 2 - cos 0 = T

QUESTION 14 The collar of mass m = 77 kg in Figure Q14 slides outwards with an initial radial velocity vo = 0.58 m-s-1 from zero initial radial position (see dashed box) along a smooth rotating shaft (see unit vector ur). The shaft rotates with constant angular speed of w = 2 rad-s-1. Determine the magnitude of the constant force F (N) that needs to be applied in the radial direction (pointing towards the centre of the shaft) in order to decelerate the collar to zero radial velocity the moment when the collar reaches a radial position r = 0.19 m. Consider motion in a horizontal plane, such that gravity can be ignored. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. Ur F m Vo Figure Q14: Rotating collar-shaft system

5. The pendulum shown below consists of a 30 kg point mass at the end of a uniform bar with mass m = 45 kg and length L = 2 m. The pendulum moves in a vertical plane while acted upon by a 500 N-m torque as shown. If the pendulum's angular velocity is 4 rad/s when 0 = 90 degrees, how much force is exerted on the pendulum by the pin at point A when 0 = 330 degrees? 500 N-m B F = 2470 N Z -52 degrees

Consider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground.   What is the kinetic energy of the system? Select all that apply.   I don't know how to get these answers.