A solid disk with a moment of inertia of I = 1/2 M R 2 about its center is initi
ID: 1466287 • Letter: A
Question
A solid disk with a moment of inertia of I = 1/2 M R2 about its center is initially spinning at 24 rad/s counter-clockwise (about its center). Three forces (ignore the weight and normal force as the disk is parallel to a horizontal surface and the weight and normal force for this case do not factor in to this problem.) are applied to the object. F1with a magnitude of 16 Newtons is applied tangentially (basically in the -x direction) at the top edge of the disk. F2with a magnitude of 11 Newtons is applied tangentially (basically in the -y direction) at the side edge of the disk. F3has an unknown magnitude and is applied tangentially (basically in the -y direction) a distance of R/4 from the center of the disk, where R is the radius of the disk. The disk takes 9 seconds to stop when these forces are applied. What is the magnitude of F3, in Newtons, if the mass of the disk is 3.1 kg and its radius is 1.9 meters?
THE CORRECT ANSWER IS 139.41. PLEASE SHOW ALL THE WORK TO GET THIS CORRECT ANSWER. THANK YOU!
A solid disk with a moment of inertia of I = 1/2 M R2 about its center is initially spinning at 24 rad/s counter-clockwise (about its center). Three forces (ignore the weight and normal force as the disk is parallel to a horizontal surface and the weight and normal force for this case do not factor in to this problem.) are applied to the object. F1with a magnitude of 16 Newtons is applied tangentially (basically in the -x direction) at the top edge of the disk. F2with a magnitude of 11 Newtons is applied tangentially (basically in the -y direction) at the side edge of the disk. F3has an unknown magnitude and is applied tangentially (basically in the -y direction) a distance of R/4 from the center of the disk, where R is the radius of the disk. The disk takes 9 seconds to stop when these forces are applied. What is the magnitude of F3, in Newtons, if the mass of the disk is 3.1 kg and its radius is 1.9 meters?
THE CORRECT ANSWER IS 139.41. PLEASE SHOW ALL THE WORK TO GET THIS CORRECT ANSWER. THANK YOU!
Explanation / Answer
angular acceleration, alfa = (w2-w1)/t
= ( 0 - 24)/9
= -2.67 rad/s^2
Moment of Inertia of disk, I = (1/2)*M*R^2
= (1/2)*3.1*1.9^2
= 5.596 N.m
Net Torque acting on disk, Tnet = F1*R + F2*R - F3*R/4
= 16*1.9 + 11*1.9 - F3*1.9/4
= 51.3 - 0.475*F3
we know, Tnet = I*alfa
51.3 - 0.475*F3 = 5.596*(-2.67)
51.3 - 0.475*F3 = -14.94
F3 = (51.3 + 14.94)/0.475
= 139.45 N <<<<<<<<<<<<<<<<<<<<<<<-------------------Answer
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