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Disk A rotates in a horizontal plane about a vertical axis at the constant rate
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Vector Mechanics for Engineers: Dynamics
- In the system shown, a 150 N collar-pulley assembly slides on a horizontal shaft with coefficient of kinetic friction uk =0.10 between the collar and the shaft, and is acted upon by a force P with a magnitude of P = 250N at an angle 0 = 30 as shown. Knowing that the assembly is initially at rest, what is the time when the velocity of collar B reaches to 3 m/s? Also, at this instant, find the tensile force in the cord and the velocity of block A.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_forwardH4.arrow_forward
- In the system that starts to move without speed, the masses of 22.2 kg each reach an angular velocity of 242 rev/min in t second at a radius of R=293 mm with the effect of the 37 N force T. Since the radius of the pulley is r = 63 mm, find t ignoring friction and all masses except the four.arrow_forwardQ2. The cord passes over a massless and frictionless pulley, as shown, carrying a mass 4m at one end and connected to a cylinder of mass 2m and radius of R that rolls on an inclined plane of 30'. What is the acceleration of the cylinder and tensions in the cable? Frictionless pulley 4m 2m ** ******* 30arrow_forwardA sheep with mass 50 kg is hung on an animal scale system which consists of a helical spring of negligible mass. The stifness (k) of the spring is 60 kN/m. During the hanging operation, the spring and sheep are displaced vertically by 20 mm below the equilibrium position. Calculate the velocity and acceleration of the sheep when it is 10mm below the rest positionarrow_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_forward5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.arrow_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
- An elongated rod of mass 4-kg has a mass of 2-kg at point A to a block moving vertically, 4-kg at point B pinned to a massive disk. The disc rotates without rolling, It is assumed that the block also moves in a frictionless channel. Please pay. The mechanism is released when stationary at θ=60º. Find the angular velocity of the rod when θ=0º.arrow_forward1. A wood block of mass mw = 200 g is projected from the ground at a speed vo = 35 m/s and at an angle 60 = 50°. When at height h= 24 m the wood block was hit by a bullet of mass m = 25 g which was moving at v= 220 m/s and at an angle 6 = 70°. After the collision, the bullet embedded itself in the block and move together and land at point A on the ground. Then they move on the ground that has coefficient of kinetic friction u: = 0.5 and start to compress a horizontal spring at point B. The distance between point À and B is 18 m and the spring constant k = 3x10? N/m. Right end of the spring is fixed, and all motions are confined in x-y plane. Wood block + Bullet Bullet Wood B block (a) Was the collision between the wood block and the bullet elastic or inelastic? Explain quantitively. (b) Find the maximum height from the ground the block with the bullet reached. (c) How far is point A from the launch point of the wood block? (d) Calculate the velocity at which the block-bullet system…arrow_forwardTwo steel balls, each of mass m = 1.84 kg, are welded to a light rod of length L = 545 mm and negligible mass and are initially at rest on a smooth horizontal surface. The distance b = 111 mm. A horizontal force of magnitude F = 27 N is suddenly applied to the rod as shown. Determine (a) the magnitude of the instantaneous acceleration a of the mass center G and (b) the magnitude of the corresponding rate 0 at which the angular velocity of the assembly about G is changing with time. Answers: a= 0 = IN PI 771 m/s² rad/s²arrow_forward
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