Learning Goal: To practice Problem-Solving Strategy 9.1 Rotational Energy. A fri

Question

Learning Goal:

To practice Problem-Solving Strategy 9.1 Rotational Energy.

A frictionless pulley has the shape of a uniform solid disk of mass 5.00kg and radius 13.0cm . A 3.10kg stone is attached to a very light wire that is wrapped around the rim of the pulley(Figure 1) , and the stone is released from rest. As it falls down, the wire unwinds without stretching or slipping, causing the pulley to rotate. How far must the stone fall so that the pulley has 9.00J of kinetic energy?

Part C

How far must the stone fall so that the pulley has 9.00J of kinetic energy?

Express your answer numerically in meters to three significant figures

Learning Goal: To practice Problem-Solving Strategy 9.1 Rotational Energy. A frictionless pulley has the shape of a uniform solid disk of mass 5.00kg and radius 13.0cm . A 3.10kg stone is attached to a very light wire that is wrapped around the rim of the pulley(Figure 1) , and the stone is released from rest. As it falls down, the wire unwinds without stretching or slipping, causing the pulley to rotate. How far must the stone fall so that the pulley has 9.00J of kinetic energy? Part C How far must the stone fall so that the pulley has 9.00J of kinetic energy? Express your answer numerically in meters to three significant figures

Explanation / Answer

Solution:

From the free body diagram, mg-T = ma

      Tr=(1/2Mr2 )

angular acceleration = =a/r

Tr =1/2 Mr2 a/r

The kinetic energy of the pulley= 9J

Kinetic energy of the stone at that point = 1/2mv2

when the distance travelled=h, velocity =v2 = 2ah

Let the stone’s initial potential energy mgh, where h= height thru which the stone dropped.

From the conservation of energy , mgh = 1/2Iw2 +1/2mv2

mgh = 9 +1/2m(2ah)

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