In the figure, a mass of 39.69 kg is attached to a light string that is wrapped

Question

In the figure, a mass of 39.69 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg · m2. The spool is suspended from the ceiling, and the mass is then released from rest a distance 8.9 m above the floor. How long does it take to reach the floor? In the figure, a mass of 39.69 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg · m2. The spool is suspended from the ceiling, and the mass is then released from rest a distance 8.9 m above the floor. How long does it take to reach the floor? A. 4.49 s B. 4.28 s C. 6.31 s D. 8.90 s E. 1.41 s

Explanation / Answer

A) 4.49 s
given

M = 39.69 kg

moment of inertia of sppol, I = 4 kg.m^2

r = 10 cm = 0.1 m

let a is the acceleration hanging body and T is the tension in the string.

T = M*g - M*a

Torque acting on spool = T*r

I*alfa = (M*g - M*a)*r

I*a/r = (M*g - M*a)*r

I*a = (M*g - M*a)*r^2

4*a = (39.69*9.8 - 39.69*a)*0.1^2

4*a = 3.89 - 0.3969*a

==> a = 3.89/4.3969

= 0.8847 m/s^2

let t is the time taken to travel 8.9 m

apply,

h = 0.5*a*t^2

==> t = sqrt(2*h/a)

= sqrt(2*8.9/0.8847)

= 4.49 s <<<<<<<<<<<<----------------Answer

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