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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
Fig. P12.68
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- A 1.4-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 8.2 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the rate v at which the speed of the slider is changing (positive if speeding up, negative if slowing down). Assume that friction is negligible. B 32 3.1' Answers: N = i Ib i ft/sec?arrow_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 weight stretches a spring 6 in. It is set in motion at a point 2 in. below its equilibrium position with a downward velocity of 2 in./sec. a. When does the weight return to its starting position? b. When does it reach its highest point? c. Show that the maximum velocity is 2sqrt(2g + 1) in./sec.arrow_forward
- 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 tube rotates in the horizontal plane at a constant rate of 0 = 4 rad/s as shown in (Figure 1). Figure Z = 4 rad/s 0.5 m 1 of 1 Part A If a 0.2-kg ball B starts at the origin O with an initial radial velocity of r = 1.5 m/s and moves outward through the tube, determine the radial and transverse components of the ball's velocity at the instant it leaves the outer end at C, r = 0.5 m. Hint: Show that the equation of motion in the direction is - 16r = 0. The solution is of the form r = Ae-4t+ Be¹t . Evaluate the integration constants A and B, and determine the time t when r = 0.5 m. Proceed to obtain vr and ve. Enter the components of the velocity separated by a comma. Express your answers in meters per second to three significant figures. Ur, υ θ = Submit Provide Feedback IVD ΑΣΦ Request Answer ↓1 vec ? m/s Next >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
- 2. 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_forwardA 7-lb collar is attached to a spring and slides without friction along a rod in the vertical plane. The spring has a constant 3.5 lb/in and 15-in. undeformed length. The dimensions are: h = 15 in. The collar is moving to the left at v = 2 in/s in the position shown. Determine the force exerted by the rod on the collar at (a) point A, (b) point B. Both A and B are on the curved portion of the rod. h www. LA h B h harrow_forwardRod OA rotates counterclockwise at a constant angular rate θ˙ = 4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r=(1.6cosθ)m. Both collars have a mass of 0.7 kg . Motion is in the horizontal plane. (Figure 1)arrow_forward
- 7. 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_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_forwardRod OA rotates counterclockwise at a constant angular rate θ˙ = 4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r=(1.6cosθ)m. Both collars have a mass of 0.55 kg . Motion is in the horizontal plane. Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant θ = 45∘ Determine the magnitude of the force that OA exerts on the other collar at the instant θ = 45∘arrow_forward
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