Write down the conservation of energy equation stating that the initial energy (

Question

Write down the conservation of energy equation stating that the initial energy (when the mass was released from rest) is equal to the final energy (when the stopwatch was turned off). Be sure to include kinetic energy (rotational and translational), potential energy, and energy dissipated due to friction (Wf). Use the following notation: m = hanging mass r = radius of shaft t = time of fall d = distance fallen v = final speed of hanging mass w = final angular speed of rotating part I = moment of inertia of whole rotating part, including support f = frictional force Now, using the relations w = v/r and v = 2d/t (make sure you understand where these come from), eliminate v and w from your energy conservation equation (i.e., rewrite the equation so that it does not contain v or w). / = frictional force Now, using the relations lj = v/r and v = Id/t (make sure you understand where these come from), eliminate v and uj from your energy conservation equation (i.e., rewrite the equation so that it does not contain v or ui). Comment

Explanation / Answer

Here, Initial energy = Final energy

=>   potential energy   = translational kinetic energy + rotational kinetic energy + work done by friction

=>    mgh = 1/2 * m v2 + 1/2 * I * w2 + Wf

=>    mgh =   1/2 * m v2 + 1/2 * I * (v/r)2 + Wf

=>    mgh =   1/2 * m (2d/t)2 + 1/2 * I * (2d/tr)2 + Wf

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