A spool of thread consists of a cylinder of radius R_1 = 4.4 cm with end caps of

Question

A spool of thread consists of a cylinder of radius R_1 = 4.4 cm with end caps of radius R_2 = 9.2 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 190 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T rightarrow = 0.580 N acting to the right is applied to the free end of the thread. For the moment of inertia treat the spool as being a solid cylinder of radius R_1, as the extended edges are thin and therefore light. What is the acceleration of the spool? Take positive to be to the right. differs from the correct answer by more than 100%. m/s^2 Determine the direction of the force of friction.

Explanation / Answer

Torque = T*R1*sin(90)

= 0.58 N*0.044 m*1

= 0.02552 N.m

I = 0.5*m*R1^2

= 0.5*0.19 kg*(0.044m)^2

= 0.000184 kg.m^2

we know, Torque = I*alfa

alfa = Torque/I

= 0.02552/0.000184

= 138.69 rad/s^2    (angular acceleration)

a = R2*alfa

= 0.092*138.69

= 12.75 m/s^2 (linear acceleration)

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