A hanging weight, with a mass of m, = 0.350 kg, is attached by a rope to a block with mass m, = 0.830 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollowcylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and thetable is u, = 0.250. At the instant shown, the block is moving with a velocity of v; = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, andthat the mass of the rope is negligible.R2R(a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown.m/s(b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance?rad/s

Given data as per the question mass m1=0.350 kgmass m2=0.830 kgmass of pulleyM=0.350 KGRadius R1=0.0200 mRadius R2=0.0300 mμk=0.250velociy of block vi=0.820 ms amoment of inertia of the pulley isI=12MR12+R22=120.3500.022+0.032=0.0002275Initial kinetic energy of the hanging blockk1=12m1v12=120.3500.8202=0.11767 jInitial potential energyU1i=mgΔr=0.350×9.8×0.7=2.401 jInitial kinetic energyk2i=12m2v12k2i=120.8300.8202k2i=0.279046jinitial rotational kinetic energyK2i=12Iω12=120.00022750.8200.03002=0.08498 jfriction force acting on the slinding block m2fs=μsm2g=0.250×0.830×9.82.0335 Naccording to law of conservation of energyk1+k2+U1+U2+ki−fsΔx=k1+k2+kf0.11767+0.279046+2.401+0+0.08498 −2.0335 ×0.700=120.35vf2+120.830vf2+120.0002275ωf21.458196=0.59vf2+120.0002275vfR121.458196=0.59vf2+0.1263 vf2vf=1.4581960.7163vf=1.42679 msbthe angular speed ωf of the pulley ωf=vfR2 ωf=1.426790.030 ωf=47.5597 rads

Engineering

Mechanical Engineering

A hanging weight, with a mass of m, = 0.350 kg, is attached by a rope to a block with mass m, = 0.830 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. R2 R (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s

A hanging weight, with a mass of m, = 0.350 kg, is attached by a rope to a block with mass m, = 0.830 kg as shown in the figure below. The rope goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R, = 0.0200 m, and an outer radius of R, = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is = 0.250. At the instant shown, the block is moving with a velocity of v, = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the rope does not stretch and does not slip on the pulley, and that the mass of the rope is negligible. R2 R (a) Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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