In the figure below, two 6.00 kg blocks are connected by a massless string over

Question

In the figure below, two 6.00 kg blocks are connected by a massless string over a pulley of radius 1.90 cm and rotational inertia 5.00 Times 10^-4 kg. m^2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.150 rad in 85.0 ms, and the acceleration of the blocks is constant. What is the magnitude of the pulley's angular acceleration? rad/s^2 What is the magnitude of either block's acceleration? m/s^2 What is the string tension T_1? N What is the string tension T_2? N

Explanation / Answer

  Pulley’s angular acceleration is

a)
=2/t^2 =2*0.15/0.085^2=41.52 rad/s^2

b)
a =r =0.0190*41.52 =0.788m/s^2

c)

mg 5e-4*41.52/0.0190–T1 = ma

T= m(g-a)=6(9.8-0.788) = 54.072N

d)
T2=T1-I/r=54.072-5e-4*41.52/0.0190=52.979 N

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