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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
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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 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_forwardPravinbhaiarrow_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
- The 4-kg collar B can slide freely on the frictionless arm OA which rotates in a vertical plane with constant angular acceleration given by ® = 10 rad/s2. The mass B is released from rest at a distance r = 0.4m from 0, find: a. The velocity of mass B along the rod OA when r = 1.0 m and 0 = 450 b. The magnitude of the horizontal force exerted on mass B by the arm OA. %3D Barrow_forwardA 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_forward2. The horizontal rod OA rotates about a vertical shaft according to the relation 6 = 3t°, where 0 and t are expressed in rad/s and seconds, respectively. A 500 g collar B is held by a cord with a breaking strength of 37 N. Neglecting friction, determine, immediately after the cord breaks: a. How long it takes for the cord to break b. The relative acceleration of the collar with respect to the rod. c. The magnitude of the horizontal force exerted on the collar by the rod. Note: the horizontal force corresponds to ég direction d. When the collar breaks free from its initial position of 0.5 m and hits the stop at A which is 0.62 m from point O, calculate the angular velocity [rad/s] at this state. *Use initial angular velocity from when cord broke in order to solve for final angular velocity using conversation of angular momentum. 0.5 marrow_forward
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