the string in a yo-yo is wound around an axle of radius 0.514 cm. The yo-yo has
ID: 2191374 • Letter: T
Question
the string in a yo-yo is wound around an axle of radius 0.514 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.111 kg and outer radius 2.00 cm. Starting from rest, it rotates and falls a distance of 1.21 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle. (a) What is the speed of the yo-yo when it reaches the distance of 1.21 m? _____m/s (b) How long does it take to fall? [Hint: The translational and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius.] _____sExplanation / Answer
Height energy lost = Kinetic energy gained KE gained = translational KE + Rotational KE KE = 0.5*0.111*V^2 + 0.5 * (0.5 * 0.111* 0.02^2) * (V/ 0.00514)^2 KE = 0.0555.V^2 + 0.4201*V^2 = 0.4756* V^2 J ?GPE = m . g . ?h = 0.111* 9.8 *1.21 = 1.32 J 1.32 = 0.4756 V^2 V = 1.66 m/s 2) Time taken = distance fallen / average velocity T = 1.21 /(1.66/2) = 1.46 s
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