In the figure, two blocks, of mass m_1 = 343 g and m_2 = 482 g, are connected by

Question

In the figure, two blocks, of mass m_1 = 343 g and m_2 = 482 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 462 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 (c) Number Units

Explanation / Answer

force on m1

in y direciton = T1-m1g = m1a

T1 = m1g + m1a .. (2)

foce on m2

m2g - T2 = m2a

T2 = m2g-m2a .. (2)

on disk

torque = I*alpha

T2*R - T1*R = I*alpha

I = MR^2/2

alpha = a/R

T2-T1 = Ma/2 ...(3)

put the value of T1 and T2 in eq (3)

a = (m2g - m1g) / (m1+m2 + M/2)

given :

m1 = 343 g = 0.343 kg

m2 = 482 g = 0.482 kg

M = 462 g = 0.462 kg

a = 1.29 m/s^2

part b )

put the value of a in eq (1)

T1 = 3.8 N

part c )

T2 = 4.1 N

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