Chapter 16, Problem 131P

The hydraulic cylinder gives pin A a constant velocity v = 2.0 m/s along its axis for an interval of motion and, in turn, causes the slotted arm to rotate about O. Determine the values of r, r, and 0 for the instant when 0 = 32°. (Hint: Recognize that all acceleration components are zero when the velocity is constant.) Answers: r = 7 = 0 = A i i i 0 34 260 mm- m/s m/s² rad/s²

The two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The acceleration of the block is aO = 5.2 m/s2. If θ˙θ˙ = 0 and θ¨θ¨ = 4.2 rad/s2 when θ = 0, find the magnitude of the acceleration of the tip A of the blade for this instant..

The boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and acceleration of the center B of the pulley for the following conditions: 0 = 30°, 0 = 7 deg/sec, 0 = 8 deg/sec², 1 = 7 ft, 1 = 2.2 ft/sec, Ï = -2.3 ft/sec². The quantities and I are the first and second time derivatives, respectively, of the length / of section AB. Express your answers as vectors in the e, and en directions. 0 Answers: VB = ав = (i 26' 8 A O er + er + B eo) ft/sec eo) ft/sec²

The center O of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. Assume a = 5.0 m/s², v = 3.0 m/s, b = 0.2 m, 0 = 45% a Answers: A VA= (i ag= (i b B b V i+i ¡+ i L--x j) m/s j) m/s²

The flywheel is rotating with an angular velocity wo 1.97 rad/s at time t 0 when a torque is applied to increase its angular velocity. If the torque is controlled so that the angle e between the total acceleration of point A on the rim and the radial line to A is equal to 54° and remains constant, determine the angular velocity and the angular acceleration at time t 0.22 s A Answer: At time t 0.22s, rad/s i W = rad/s2 a =

The two V-belt pulleys form an integral unit and rotate about the fixed axis at O. At a certain instant, point A on the belt of the smaller pulley with a distance of DA = 143 mm has a velocity VA = 2.8 m/s, and point B on the belt of the larger pulley with a distance of DB = 900 mm has an acceleration ag = 43 m/s? as shown. For this instant determine the magnitude of the acceleration ac of point C in m/s? if Rc = 374 mm. ав В DB UA Rc A DA

b) Find the angular velocity and angular acceleration of disc B shown below, which is spinningatthe constant rate of ω2 = 90/πrpm. The disc is attached to collar A, which is rotating at the angular speed of ω1 = 5/π rpm, with the angular speed increasing at 0.5/π rpm/sec. Rod AB which connects the disc to the collar ispinned to the collar at A. The rod makes an angle of θ = 300 with the vertical, which is increasing at a constant rate of20/π0/sec.Express theAngularvelocityAcceleration of the disc in terms of a reference frame attached to thecollar.

The small collar A is sliding on the bent bar with speed u = 1.5 m/s relative to the bar as shown. The distances are L= 2.60 m and d = 0.77 m. Simultaneously, the bar is rotating with angular velocity w = 2.33 rad/s about the fixed pivot B. Take the x-y axes to be fixed to the bar and determine the Coriolis acceleration acor of the slider for the instant represented. Interpret your result. В Answer: acor = ( i i+ i j) m/s? B.

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