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Quiz_4_solutions_web - Problem 1 An Atwood’s machine...

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Problem 1 An Atwood’s machine consists of a pulley which can be approximated as a disk of radius 10cm and mass 2kg and a rope of negligible mass which connects a mass of 4kg to one of 1kg. The system is released from rest with the 4 kg mass 1.5m from the floor and the 1kg mass on the floor. a) What is the speed of the blocks just before the 4kg mass hits the floor? b) How long does it take for the 4kg mass to reach the floor? The rope does not slip on the pulley and the moment of inertia of a solid disk is ½ MR 2 . 1) Using conservation of energy Apply the conservation of energy, taking the zero of potential energy to be at the floor. Initial energy is the potential energy of the 4kg mass Final energy is the kinetic energy of the two masses plus the kinetic energy of the pulley plus the potential energy of the 1kg mass. Let v be the final speed of the blocks and ω the angular velocity of the pulley. Then v=R ω Intial Energy =m 1 gh Final energy = ½ m 1 v 2 + ½ m 2 v 2 + ½ I ω 2 +m 2 gh Conservation of energy says the initial energy equals the final energy Substitute for ω and I and solve for v m 1 gh= ½ m 1 v 2 + ½ m 2 v 2 + ½ ½ MR 2 v 2 /R 2 + m 2 gh ½ v 2 (m 1 +m 2 + ½ M)=gh(m 1 -m 2 ) v 2 =2x9.8x1.5x3/6 v=3.8m/s Let the constant acceleration during the motion = a v 2 =v 0 2 +2as =2as M m 1 R m 2 h = 0 h
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The time taken is given by v=v 0 +at t=v/a =v2s/v 2 =2s/v=2x1.5/3.8=0.8s 2) Using the second law
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This note was uploaded on 10/07/2009 for the course PHYS 1301W taught by Professor Marshak during the Fall '08 term at Minnesota.

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Quiz_4_solutions_web - Problem 1 An Atwood’s machine...

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