Answer:
116 s
Explanation:
We can convert the 23 rotation per minute to radian per second knowing each rotation is 2π and each minute has 60 seconds.
[tex]\omega_0 = 2\pi*23/60 = 2.41 rad/s[/tex]
The torque generated by Jacob at the outer rim in the direction of motion
[tex]T_J = F_JR_J = 12.3 * 3.3 = 40.59 Nm[/tex]
The torque generated by Sophia at r = 3.1 m that hampers the motion is
[tex]T_S = F_Sr = 21.2*3.1 = 65.72 Nm[/tex]
The net torque is
[tex]T = T_S - T_J = 65.72 - 40.59 = 25.13 Nm[/tex]
The moment of inertia of the solid disk merry-go-round is:
[tex]I = mR^2/2[/tex]
Where m = 223 kg is the disk mass and R = 3.3 m is the radius of the disk.
[tex] I = 223*3.3^2/2 = 1214.235 kgm^2[/tex]
So the angular deceleration is
[tex]\alpha = T / I = 25.13 / 1214.235 = 0.0207 rad/s^2[/tex]
If the initial angular speed is 2.41, the time it'd take to decelerate to rest is
[tex]t = \Delta \omega / \alpha = \frac{0 - 2.41}{-0.0207} = 116 s[/tex]
