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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
- 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_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
- 1. 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_forwardGear A with radius 0.018 m is moving with velocity wn = 0.12 rad/s clockwise, with a constant angular acceleration aa = 0.07 rad/s?. B and D are rigidly attached to each other and the radius of B is 0.24m and the radius of D is 0.09m. The weight of the block Cis 191 Newtons. Determine the time in seconds that it takes block C to move up 9 meters. Also answer the following at exactly that time: 1. Draw the complete and clear FBD of the block C. Indicate two sides of the FBD with all forces and mass x accelerations, label all of them. 2. Find the velocity of point P and find the acceleration of point P that belongs to B 3. Find the number of rotations of B. 4. Find the acceleration of C; then, determine the tension in the rope from the FBD of C.arrow_forwardA disk of radius R = 0.5833 ft spins at a constant angular speed of o = 52.36 rad/s in the clockwise direction. If the disk is released from rest far above the ground, what are the speed and acceleration of the disk's top C after it has fallen h = 3 ft? (g= 32.2 ft/s²) Hint: Speed v of an object falling from R the rest can be determined from its falling distance h by, v = /2gharrow_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_forwardThe system shown begins its motion from rest and each component moves with a constant acceleration.If the relative acceleration of block C with respect to collar B is 30 mm / s ^ 2 downwards, and the relative acceleration of block A with respect to block D is 55 mm / s ^ 2 downwards.Answers:1)The speed of block A after 5 s2)The change in the position of block B after 3 sarrow_forwardPulley B is being driven by the motorized pulley A that is rotating at ωA =20 rad/s. At time t = 0, the current in the motor is cut off, and friction in the bearings causes the pulleys to coast to a stop. The angular acceleration of A during the deceleration is αA = −2.5t rad/s2, where t is in seconds. Assuming that the drive belt does not slip on the pulleys, determine (1) the angular velocity of B as a function of time; (2) the angular displacement of B during the period of coasting; and (3) the acceleration of point C on the straight portion of the belt as a function of time.Note: R1 as your last three numbers of your university ID, and R2 is half of that. Units in mmarrow_forward
- A block of mass m1 is located on an inclined plane θ and attached by a rope passing over a pulley with a weight of mass m2. If m1 > m2 find the tension and the acceleration.arrow_forward2. For a short period of time, the motor turns gear A with a constant angular acceleration, starting from rest. The cord is wrapped around pulley D which is rigidly attached to gear B. 4) if the radii are: ƒÃ = 65 mm, r = 205 mm, and = rp¹ 95 mm, the constant angular acceleration of gear A, AA is 3.1 rad/s², determine the linear velocity of the cylinder C, in m/s, after 2 seconds. Hint, the cylinder C has the same linear velocity as point P'on the pulley D. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. OLA A P Your Answer: 1'B B Answerarrow_forwardThe spring-mounted 0.90-kg collar A oscillates along the horizontal rod, which is rotating at the constant angular rate 0 = 6.2 rad/s. At a certain instant, r is increasing at the rate of 790 mm/s. If the coefficient of kinetic friction between the collar and the rod is 0.68, calculate the friction force Fexerted by the rod on the collar at this instant. Vertical (ונננננ Answer: F = i Narrow_forward
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