(a) What is the acceleration of the spool? Take positive to be to the right. A s
ID: 1286811 • Letter: #
Question
(a) What is the acceleration of the spool? Take positive to be to the right.
A spool of thread consists of a cylinder of radius R1 = 6.3 cm with end caps of radius R2 = 11.4 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 300 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force vector T = 0.680 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 R1, as the extended edges are thin and therefore light. Please show work and how you got to the answer!! (a) What is the acceleration of the spool? Take positive to be to the right. (b) Determine the direction of the force of friction.Explanation / Answer
Torque = T*R1*sin(90)
= 0.68*0.063*1
= 0.04284 N.m
I = 0.5*m*R1^2
= 0.5*0.3*0.063^2
= 0.0059535 kg.m^2
we know, Torque = I*alfa
alfa = Torque/I
= 0.04284/0.0059535
= 7.196 rad/s^2 (angular acceleration)
a = R2*alfa
= 0.114*7.196
= 0.82 m/s^2 (linear acceleration)
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