How Much Energy Is Lost to Friction in a Spool of Wire System?

AI Thread Summary
To calculate the energy lost to friction in the spool of wire system, first determine the change in potential energy as the mass falls, which is given by the formula PE = M * g * D. Next, calculate the kinetic energy of the mass after falling, using KE = 0.5 * M * v^2. The energy lost to friction can be found by subtracting the kinetic energy from the potential energy. It’s important to consider the moment of inertia of the spool and the rotational dynamics involved. This approach will yield the total energy lost to friction during the descent of the mass.
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Homework Statement


A spool of thin wire (with inner radius r = 0.40 m, outer radius R = 0.55 m, and moment of inertia I_cm = 0.7139 kg*m^2) pivots on a shaft. The wire is pulled down by a mass M = 1.350 kg. After falling a distance D = 0.550 m, starting from rest, the mass has a speed of v = 65.4 cm/s. Calculate the energy lost to friction during that time.


im not really sure how to do this. i would like any ideas.
 
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Consider the change in potential energy.
 

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