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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Use conservation of energy to determine the angular speed of the spool shown in Figure P8.58 after the 3.00-kg bucket has fallen 4.00 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.

images

Figure P8.58

To determine
The angular speed of the spool.

Explanation

Given info: The mass of the bucket is 3.00kg , mass of the spool is 5.00kg , and the radius of the spool is 0.600m .

Explanation: The gravitational potential energy of the bucket is converted as sum of rotational and translational kinetic energies after its release from rest. Now the moment of inertia of the spool is I=MR2/2 and the translational speed of the spool is vt=Rω . As stated above, the energy conservation is KEt,f+KEr,f+PEg,f=KEt,i+KEr,i+PEg,i and thus, the bucket starts from rest, the expression of conservation of energy is modified as Mvt2/2+Iωf2/2+mgyf=0+0+mgyi . This expression is going to be rearranged for the angular speed of the spool.

The formula for the angular speed of the spool is,

ωf=2mg(yiyf)(m+M2)R2

  • m is mass of the bucket

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