How Much Energy Is Lost to Friction When a Mass Pulls Down a Spool of Wire?

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To determine the energy lost to friction when a mass pulls down a spool of wire, one must analyze the energy transformations involved. The gravitational potential energy of the mass is converted into kinetic energy and rotational energy of the spool as it descends. The conservation of energy principle can be applied to relate these energies, accounting for the energy lost to friction. The problem requires calculating the initial potential energy, the final kinetic energy, and the rotational energy to find the friction loss. A clear understanding of these energy types is essential for solving the problem effectively.
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Homework Statement


A spool of thin wire (with inner radius r = 0.45 m, outer radius R = 0.60 m, and moment of inertia Icm = 0.91 kg*m2 pivots on a shaft. The wire is pulled down by a mass M = 1.35 kg. After falling a distance D = 0.52 m, starting from rest, the mass has a speed of v = 79.900 cm/s. Calculate the energy lost to friction during that time. http://schubert.tmcc.edu/res/msu/physicslib/msuphysicslib/20_Rot2_E_Trq_Accel/graphics/prob22_pulleyD.gif


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The Attempt at a Solution



I have been having a lot of trouble with these rotation problems and I am not sure where to start on this. Any assistance would be appreciated.
 
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Consider the types of energy involved. You start with the gravitational PE of the mass, and as it falls you lose that and get KE plus the rotational energy of the spinning spool. Write out a law of conservation of energy for those.
 

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