A cube of mass M = 500 g and side length 30 mm is free to spin on anaxis through

Question

A cube of massM = 500 g and side length 30 mm is free to spin on anaxis through the center of one face. A massless pulley on this axishas a diameter of 2r = 10 mm. Anobject with m= 50 g is hung from a string wrappedaround the pulley. The assembly is released from rest. Ignorefriction. a) What is the time to unwind L = 30 cm ofstring. Hint: Find the angular acceleration of the apparatus, thenfind the time using Dq= (1/2)aDt2 where Dq= L/r. b) What is the kineticenergy of the spinning block after the string unwinds? Use energymethods. Please showme step by step how to do this. Thanks! A cube of massM = 500 g and side length 30 mm is free to spin on anaxis through the center of one face. A massless pulley on this axishas a diameter of 2r = 10 mm. Anobject with m= 50 g is hung from a string wrappedaround the pulley. The assembly is released from rest. Ignorefriction. a) What is the time to unwind L = 30 cm ofstring. Hint: Find the angular acceleration of the apparatus, thenfind the time using Dq= (1/2)aDt2 where Dq= L/r. b) What is the kineticenergy of the spinning block after the string unwinds? Use energymethods. Please showme step by step how to do this. Thanks! a) What is the time to unwind L = 30 cm ofstring. Hint: Find the angular acceleration of the apparatus, thenfind the time using Dq= (1/2)aDt2 where Dq= L/r. b) What is the kineticenergy of the spinning block after the string unwinds? Use energymethods. Please showme step by step how to do this. Thanks! Please showme step by step how to do this. Thanks!

Explanation / Answer

I = .500*(.03/2)2/6 moment of inertia ofcube same as that of a square                        plate about axis thru center I = 1.875 * 10E-5 kg m2 m a = m g - T    acceleration of mass m and T = tension m a = m g - T    acceleration of mass m and T = tension T r = I m a = m g - I / r = m g - I a / r2 a = m g / (m + I/r2)= .05*9.8/(.05 +1.875*10E-5/.0052) a = .6125 m/s2 Just use L = 1/2 a t2 where L = .3 m to get timet Then = t = a t / r   and KE = 1/2 I2

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