In the figure, two blocks, of mass m 1 = 363 g and m 2 = 499 g, are connected by

Question

In the figure, two blocks, of mass m1 = 363 g and m2 = 499 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 557 g and radius R = 11.5 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 T1 in the cord at the left and (c) the tension T2 in the cord at the right.

(a)

Number

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This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

(b)

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This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

(c)

Number

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This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

(a)

Number

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This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

Explanation / Answer

Apply Newton second to the block 1

T1- m1g = m1a

T1= m1 a+ m1g

to the block2

m2g -T2 = m2 a

T2 = m2g- m2a

for pulley

T2 R- T1 R = I alpha

T2 R - T1 R = MR^2/2 * ( a/R)

T2- T1 = Ma/2

m2g- m2a-m1 a- m1g= Ma/2

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

= (0.499-0.363)9.8/(0.557/2 + 0.499+0.363)

=1.168 m/s^2

(b)

T1 = 0.363(1.16+9.8) = 3.98 N

(c)

T2 = 0.499(9.8-1.168) = 4.3 N

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