A block of mass m1 = 6 kg on a rough 30°-inclined plane is connected to...

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Physics

A block of mass m1 = 6 kg on a rough 30°-inclined plane isconnected to a 4-kg mass (m2) by a string of negligible masspassing over a pulley shaped like a ring. The 2-kg pulley hasradius 20 cm and rotates about its symmetry axis of rotation. Thestring causes the blocks and the pulley to rotate without slippingand without friction. The 6-kg block (m1) on the 30°slope isinitially pressed against a spring near the bottom of a long roughincline, compressing the spring by 50 cm. The spring is notattached to the block and has a spring constant is 500 N/m. Whenthe system is released, the spring returns to its equilibriumlength as it projects the 6-kg block (m1) toward the top of theincline. Assume that the spring just loses contact with the block(m1) at the instant it returns to its equilibrium length. Thecoefficient of kinetic friction between the block (m1) and thesurface of the incline is 0.2. By considering the conservation ofenergy and any other suitable methods: (a) Calculate the speed ofthe blocks at the instant the spring first returns to itsequilibrium length. [v = 3.2 m/s] (b) What is the total angularmomentum of the system when the spring first returns to itsequilibrium length? [7.7 kg.m2/s] (c) By considering the totalangular momentum of the system, find the rate of change of theangular momentum of the system after the blocks lose contact withthe spring. [-0.08 m.N] (d) What is the net torque causing theangular acceleration of the system after the blocks lose contactwith the spring? [-0.08 m.N]

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