A pulley on a frictionless axle has the shape of a uniform solid disk of mass 2.10 kg and radius 20.0 cm. A 1.90 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Figure 1), and the system is released from rest. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of An unwinding cable ii. Part A How far must the stone fall so that the pulley has 4.50 J of kinetic energy? Express your answer with the appropriate units. THA ΠΑ 2 ha Value Units Submit Request Answer Part B What percent of the total kinetic energy does the pulley have? Express your answer in percent.

According to this law, energy can only be converted from one form to another and it can neither be created nor destroyed. Total energy before and after the event remains conserved.

Given, the mass of the pulley, M = 2.10 Kg

The mass of stone, m = 1.90 Kg

The radius of the pulley, R = 20 cm

The kinetic energy of the pulley = 4.50 J

The kinetic energy of the pulley, I = (1/2) I ω²

[tex]{\displaystyle \frac{1}{2} I\omega^2 = 4.50\; J[/tex]

[tex]{\displaystyle \frac{1}{4} M v^2 = 4.50\; J[/tex]

[tex]{\displaystyle \frac{1}{4} \times 2.10 \times v^2 = 4.50\; J[/tex]

v² = 8.57 m²/s²

From the law of conservation of energy:

KE(pulley) + KE (stone) + PE (mass) = 0

[tex]{\displaystyle 4.50\; J + \frac{1}{2} m v^2-mgh =0[/tex]

[tex]{\displaystyle 4.50\; + \frac{1}{2} (1.9) \times 8.57=1.9 \times 9.8 \times h[/tex]

h = 0.68 m

The percent of total kinetic energy is given by:

[tex]\% KE_p = \frac{KE_p}{KE_{total}}\times 100[/tex]

[tex]\% KE_p = \frac{4.50}{4.50 + \frac{1}{2} \times 1.9\times 8.57}\times 100[/tex]

[tex]\% KE_p = 35.6 \%[/tex]

Learn more about the law of conservation of energy, here:

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