A frictionless pulley has the shape of a uniform solid disk of mass 2.10 kg and

Question

A frictionless pulley has the shape of a uniform solid disk of mass 2.10 kg and radius 10 cm. A 1.20 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (the figure (Figure 1) ), and the system is released from rest.

Part A

How far must the stone fall so that the pulley has 5.80 J of kinetic energy?

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Part B

What percent of the total kinetic energy does the pulley have?
.

A frictionless pulley has the shape of a uniform solid disk of mass 2.10 kg and radius 10 cm. A 1.20 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (the figure (Figure 1) ), and the system is released from rest.

Part A

How far must the stone fall so that the pulley has 5.80 J of kinetic energy?

h=   m  

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Incorrect; Try Again; 11 attempts remaining

Part B

What percent of the total kinetic energy does the pulley have?
.

KpKtot= %

Explanation / Answer

  KE = (1/2) I w^2

= (1/2) (1/2)MR^2 * w^2

= (1/4) Mv^2,

where v = linear velocity of the stone

5.80 = (1/4) * 2.10 * v^2

v = sqrt(5.80*4/2.10) = 3.32 m/s

(a) Let d = distance by which the stone must fall

loss of PE of the stone = gain of KE of the stone + pulley

(1.20) * 9.81 * d = (1/2) * (1.20) * (3.32)^2 + 5.80

d =12.41 / (1.20 * 9.81) = 1.05 m

(b)
% of total KE that the pulley has

= 5.8/(5.8+6.61)*100

= 46.73

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