The stone will fall 0.68 m so that the pulley has 4.50 J of kinetic energy.
The percent of the total kinetic energy of the pulley is 35.6 %.
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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