In the figure, two blocks, of mass m_1 = 211 g and m_2 = 339 g, are connected by

Question

In the figure, two blocks, of mass m_1 = 211 g and m_2 = 339 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 468 g and radius R = 13.5 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T_1 in the cord at the left and (c) the tension T_2 in the cord at the right. (a) Number Units (b) Number Units

Explanation / Answer

T1 = m1 g + m1 a ------(1)

T2 = m2 g + m2 a ------(2)

a = m2 g - m1 g / (m1 + m2 + 1/2 M)

= ( 0.339 * 9.8 - 0.211 * 9.81 ) / (0.339 + 0.211 + 1/2 (0.468))

a = 1.6 m/s2

substitute a in above equations

T1 = m1 g + m1 a

= (0.211 * 9.81) + (0.211 * 1.6)

T1 = 2.41 N

T2 = m2 g + m2 a

= (0.339 * 9.8) + (0.339 * 1.6)

T2 = 3.86 N

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