A block of mass m sliding on a frictionaless table is attachedto a string that p

Question

A block of mass m sliding on a frictionaless table is attachedto a string that passes through a narrow hole through the center ofthe table. The block is sliding with speed Vsub0 in a circleof radius rsub0. Find. A.) the angular momentum of the block B.) The kinetic energy of the block C.) The tension in the string D.) A student under the table now slowly pulls the stringdownward. How much work is required to reduce the radius of thecircle from rsub0 to rsub0/2 ? A block of mass m sliding on a frictionaless table is attachedto a string that passes through a narrow hole through the center ofthe table. The block is sliding with speed Vsub0 in a circleof radius rsub0. Find. A.) the angular momentum of the block B.) The kinetic energy of the block C.) The tension in the string D.) A student under the table now slowly pulls the stringdownward. How much work is required to reduce the radius of thecircle from rsub0 to rsub0/2 ?

Explanation / Answer

A) The angular momentum of the block                   L = m vo ro B) The kinetic energy of the block                   KE= 0.5 m vo2 C) The tension in the string is                     T= 0.5  m vo2/ ro D) Workdone is equal to change in kinetic energy of theblock            W= KE                = Kf - Ki     We know that              K = L / 2I           W = (L / 2If - L / 2Ii ) Where If = m(0.5 ro)2               Ii = m ro2 Substituting we get                  W = -0.66 L / mro2 Substituting we get                  W = -0.66 L / mro2

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