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Two 2.6-Ib collars A and B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about CD. The two collars are connected by a cord running over a pulley that is attached to the frame at O, and a stop prevents collar B from moving. The frame is rotating at the rate
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Vector Mechanics for Engineers: Dynamics
- The shown collar has a mass of 1.4 kg and moves along the smooth vertical rod defined by the equation de = 1.4 rad/sec and dt d'e = 0.25 rad/sec, r=2.0 0 m with e in rad. Knowing that at this instant 0=45°, di? a, =-2.579 m/s and ag=8.233 m/s? Note: Angle y is the angle between positive unit radial and positive unit tangent vectors with w =38.15° Un A-Determine the magnitude of the tangential force F acting on the collar B-Determine the magnitude of the reaction between rod and collararrow_forwardAn elongated rod of mass 4-kg has a mass of 2-kg at point A to a block moving vertically, 4-kg at point B pinned to a massive disk. The disc rotates without rolling, It is assumed that the block also moves in a frictionless channel. Please pay. The mechanism is released when stationary at θ=60º. Find the angular velocity of the rod when θ=0º.arrow_forwardA 1-m-long uniform slender bar AB has an angular velocity of 12 rad/s and its center of gravity has a velocity of 2 m/s as shown. About which point is the angular momentum of A smallest at this instant? P1 P2 P3 P4 It is the same about all the points.arrow_forward
- The double pulley shown in the figure has a mass of 3 kg and a radius of 100 mm rotation. Knowing that when the pulley is at rest, it is applied to the cable in B, a force P of magnitude equal to 24N, determine the speed of the center of the pulley after 1.5 s and the tensile force on cable C.arrow_forwardTwo disks each have a mass of 5 kg and a radius of 300 mm. They spin as shown at the rate of w1 = 1200 rpm about a rod AB of negligible mass that rotates about the horizontal z axis at the rate of w2. Determine the maximum allowed value of w2 if the magnitudes of the dynamic reactions at points C and D are not to exceed 350 N each.arrow_forwardANSWER= 3.621790, -9.99745arrow_forward
- Two uniform cylinders, each of mass m= 9.5 kg and radius r= 125 mm, are connected by a belt as shown. The system is released from rest when t = 0. B A Determine the velocity of the center of cylinder A at t = 4.4 s. The velocity of the center of cylinder A is 3 m/s ↓.arrow_forwardForce-Mass-Acceleration Method (General Plane Motion, GPM) vA=X=8ft/sarrow_forwardThe figure shows a schematic of a simple Watt governor mechanism with the spindle 0102 rotating at an angular velocity w about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O₁ is denoted by h. The value of h = 400 mm at a certain w. If w is doubled, the value of h will be mm. (0) g = 9.8 m/s₂ h Spindle O Q Sleeve (QR) Cylindrical Joint R Sarrow_forward
- The wheel W of radius R = 1.4 m rolls without slip on a horizontal surface.A bar AB of length L = 3.7 m is pin-connected to the center of the wheel and to a sliderA constrained to move along a vertical guide. Point C is the bar’s midpoint. Determinethe general relation expressing the acceleration of the slider A as a function of θ, L, R,the angular velocity of the wheel αW , and the angular acceleration of the wheel ωW .arrow_forwardThe 1.8-kg uniform bar rotates in the vertical plane about the pin at O.When the bar is in the position shown, its angular velocity is 4 rad/s, clockwise. For this position, find (a) the angular acceleration of the bar; and (b) the magnitude of the pin reaction at O.arrow_forward5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.arrow_forward
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