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Applied Dynamics Mechanical Engineering, UPB April 16, 2018 This is a list of problems taken from [1] • [3/11]Calculate the vertical acceleration a of the 100-lb cylinder for each of the two cases illustrated. Neglect friction and the mass of the pulleys.

Figure 1: Problem [3/11] • [3/18] The sliders A and B are connected by a light rigid bar of lengthl = 0.5m and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position where xA = 0.4m, the velocity of A is vA = 0.9m/s to the right. Determine the acceleration of each slider and the force in the bar at this instant

Figure 2: Problem [3/32] • [3/35] The nonlinear spring has a tensile force-deflection relationship given by Fs = 150x + 400x2 , where x is in meters and Fs is in newtons. Determine the acceleration of the 6-kg block if it is released from rest at (a) x = 50mm and (b) x = 100mm.

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Figure 3: Problem [3/35] • [3/36] Two configurations for raising an elevator are shown. Elevator A with attached hoisting motor and drum has a total mass of 900 kg. Elevator B without motor and drum also has a mass of 900 kg. If the motor supplies a constant torque of 600 N m to its 250 mm diameter drum for 2 s in each case, select the configuration which results in the greater upward acceleration and determine the corresponding velocity v of the elevator 1.2 s after it starts from rest. The mass of the motorized drum is small, thus permitting it to be analyzed as though it were in equilibrium. Neglect the mass of cables and pulleys and all friction.

Figure 4: Problem [2/23] • [3/74] The robot arm is elevating and extending simultaneously. At a given instant, θ = 30◦ , θ˙ = 40 deg/s, θ¨ = 120 deg/s2 , l = 0.5 m, l˙ = 0.4 m/s, and l¨ = −0.3 m/s2 . Compute the radial and transverse forces Fr and Fθ that the arm must exert on the gripped part P , which has a mass of 1.2 kg. Compare with the case of static equilibrium in the same position.

Figure 5: Problem [3/74] 2

• [6/67] The robotic device consists of the stationary pedestal OA, arm AB pivoted at A, and arm BC pivoted at B. The rotation axes are normal to the plane of the figure. Estimate (a) the moment MA applied to arm AB required to rotate it about joint A at 4 rad/s2 counterclockwise from the position shown with joint B locked and (b) the moment MB applied to arm BC required to rotate it about joint B at the same rate with joint A locked. The mass of arm AB is 25 kg and that of BC is 4 kg, with the stationary portion of joint A excluded entirely and the mass of joint B divided equally between the two arms. Assume that the centers of mass G1 and G2 are in the geometric centers of the arms and model the arms as slender rods.

Figure 6: Problem [6/67] • [6/75] Above the earth’s atmosphere at an altitude of 400 km where the acceleration due to gravity is 8.69 m/s2 , a certain rocket has a total remaining mass of 300 kg and is directed 30◦ from the vertical. If the thrust T from the rocket motor is 4 kN and if the rocket nozzle is tilted through an angle of 1◦ as shown, calculate the angular acceleration α of the rocket and the x− and y− components of the acceleration of its mass center G. The rocket has a centroidal radius of gyration of 1.5 m.

Figure 7: Problem [6/75] • [6/88] The circular disk of 200-mm radius has a mass of 25 kg with centroidal radius of gyration k = 175mm and has a concentric circular groove of 75mm radius cut into it. A steady force T is applied at an angle θ to a cord wrapped around the groove as shown. If T = 30N, θ = 0 3

µs = 0.1 and µk = 0.08, determine the angular acceleration of the disk, the acceleration a of its mass center G, and the friction forceF which the surface exerts on the disk.

Figure 8: Problem [6/88] • [6/8] A car door is inadvertently left slightly open when the brakes are applied to give the car a constant rearward acceleration a. Derive expressions for the angular velocity of the door as it swings past the 90◦ position and the components of the hinge reactions for any value of θ. The mass of the door is m, its mass center is a distance r from the hinge axis O, and the radius of gyration about O is kO .

Figure 9: Problem [6/8]

References [1] J. Meriam and L. Kraige, Engineering Mechanichs Dynamics, 7th ed. Inc, 2012, vol. 2.

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