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The 3-kg collar B slides on the frictionless arm AA'. The arm is attached to drum D and rotates about O in a horizontal plane at the rate
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Chapter 12 Solutions
Vector Mechanics for Engineers: Dynamics
- Q2) The slotted arm pivots about O and maintains the relation between the motions of sliders A and B and their control rods. Each small pivoted block is pinned to its respective slider and is constrained to slide in its rotating slot. Show that the displacement x is proportional to the reciprocal of y. Then estab- lish the relation between the velocities vA and vg. Also, if v, is constant for a short interval of motion, determine the acceleration of B. b y 'Barrow_forwardThe 3-kg collar B slides on the frictionless arm AA’. The arm is attached to drum D and rotates about O in a horizontal plane at the rate 0=0.75t, where 0 and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s. Knowing that at t= 0, r= 0, determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA,.arrow_forwardA spring is connected between the 1-kg slider A and the frame. The spring has a stiffness of 5N/m and it is undeformed when x = 0.1m. Knowing that the frame is rotating in the horizontal plane about O at the constant angularspeed ˙ θ = 2 rad/s, determine the distance x. Neglect friction.arrow_forward
- box anserarrow_forward5. The slider P can be moved inward by means of the string S, while the slotted arm rotates about point O. The angular position of the arm is given 12 where e is in radians and t is in 20 by 0 = 0.81 - %3D seconds. The slider is at r 1.6 m when t = 0 and thereafter is drawn inward at the constant rate of 0.2 m/s. Determine the magnitude and direction (expressed by the angle relative to the positive x- axis) of the velocity and acceleration of the slider when t= 4 s. %3D Ans. 0.377 m/s, 259.5°; 0.272 m/s, 19.4° y 1. Sarrow_forwardThe mass B is attached to the arm that rotates in the horizontal planeabout a pin in collar A. A motor in A keeps the angular speed of the arm constant at ˙ θ = 2.4 rad/s. Determine the velocity and acceleration of A as functions of the angle θ. Assume that vA = 0 when θ = 0. Friction and the mass of the rotating arm can be neglected.arrow_forward
- 7. The 540-lb cylinder at A is hoisted using the motor and the pulley system shown. The speed of point B on the cable is increased at a constant rate from zero to Bv_B = 30 ft/sft/s in t = 9 sarrow_forward7. The 400-lb cylinder at A is hoisted using the motor and the pulley system shown. If the speed of point B on the cable is increased at a constant rate from zero to vg = 10/s in t = 5 s, determine the tension in the cable at B to cause the motion. (Practice at Home) B Aarrow_forwardВ (3) A smooth can C, having a mass of 3 kg, is lifted from Ö=2rad/s² é = 0.5 rad/s a feed at A to a ramp at B by a rotating rod. If the rod rotates angular velocity of 0=0.5 rad/s and Ö=2rad/s2, determine the forces which the rod and 600 mm circular ramp in the vertical plane exert on the can at the instant 0=30°. Neglect the friction and the size of the can so that r = (1.2cos6) m. The ramp -600 mm- from A to B is circular, having a radius of 600 mm. m-5 kgarrow_forward
- A brass (nonmagnetic) block A and a steel magnet B are in static equilibrium in a brass tube under the magnetic repelling force of another steel magnet, C. The magnet B is located a distance x =d, from C. If block A is suddenly removed, and the acceleration of block B is: k a =-g+ where g andk are known constants. Determine: a. the velocity, v, as a function of the position x and the known parameters (g,k,d,), and b. the position, x, when the velocity is maximum in terms of the known parameters (g,k,d,). Вarrow_forward= The rigid assembly which consists of light rods of lengths a = 0.3 m and b = 0.5 m and two 1.2-kg spheres rotates freely about a vertical axis. A couple M 0.2t N.m, where t is time in seconds, is applied to the assembly. Determine the angular velocity of the assembly at t = 10 s if (a) the assembly is initially at rest, and (b) the assembly initially rotates with an angular velocity wo rad/s as shown. Treat the small spheres as particles. (w = 24.5 rad/s, w = 20.5 rad/s) a M b = = 4 m ωο marrow_forward1. Two children A and B, each having a mass 30kg, sit at the edge of the merry-go-round which is rotating with angular velocity @ = 2 rad/s. Excluding the children, the merry-go-round has a mass 180 kg and a radius of gyration k₂ = 0.8m. Determine the angular velocity of the merry-go-round if A jumps off horizontally in the -n direction (away from the merry-go-gound) with a speed of 3 m/s, measured with respect to the merry-go-round. After A jumps off, B then jumps off horizontally in the +t direction with a speed of 3 m/s, measured with respect to the merry-go-round - what is the merry-go-round's angular velocity now? Neglect friction and the size of each child. 1m 1m B w = 2 rad/sarrow_forward
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