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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
- 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_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_forward
- A 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_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_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_forward
- В (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_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_forwardThe two blocks A and B each have a mass of 440 g . The blocks are fixed to the horizontal rods, and their initial velocity along the circular path is 2 m/s. A couple moment of M = (0.6) N⋅m is applied about CD of the frame. The mass of the frame is negligible, and it is free to rotate about CD. Neglect the size of the blocks. a) Determine the speed of the blocks when t = 3 s. v = ?arrow_forward
- The slender bar AB with a mass of 60 kg and a length of 4 m is secured by a cable at C, and pivoted to the back of a truck at A. When the truck starts from rest creating an acceleration of 5 m/sec² on the bar in the direction of the arrow, calculate the magnitude of the tension in the cable. Present your answer in Newtons using 3 significant figures. В. 4 m 60° A -2 marrow_forwardA motorcycle and rider have a combined mass of 350kg. The vehicle's velocity is 100 km/hr. The rider is to go up a hill incline of 10 meters. The wheels each have a mass of 20 kg and a diameter of 500mm. The wheel design consists of 6 spokes with a mass of 0.5 kg for each spoke. a. Determine the vehicle's velocity at the top of the hill, assuming it was a rolling vehicle with engine being turned off. a. Indicate the vehicle's velocity at each meter through the climb. b. Explain the transfer energy and how this affects the behaviour of the system. At another point in its journey, the motorcycle and rider travel at 80 km/h around a left-hand bend of radius 30m. Calculate: a) The angular velocity of each wheel. b) The moment of inertia of each wheel. c) The angular momentum of the wheel prior to entering the bend. d) The magnitude of the gyroscopic torque produced on the bike as the rider is driving around the bend. What is the effect and why is it important to calculate the gyroscopic…arrow_forwardDynamic Lecture: The 2 kg BC ring can only move left and right on the frictionless rigid arm. Ring BC is connected to springs with spring constants k = 300 N / m and k ′ = 200 N / m at points AB and CD. The unstretched length of both springs is 600 mm. Since it is known that the springs are not tensioned and starts from rest, find the velocity of the ring BC at the moment when the external force F is applied 200 mm.arrow_forward
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