Answer:
This question can be solved by using the work-energy theorem.
[tex]W_{total} = \Delta K[/tex]
[tex]Fx = \frac{1}{2}I\omega^2 - 0[/tex]
[tex]5\times 1.25 = \frac{1}{2}(0.0352)\omega^2\\\omega = 18.84 ~rad/s\\v = \omega r = 18.84 \times (0.125) = 2.35 ~ m/s[/tex]
Explanation:
The work energy theorem tells us that the total work done on an object is equal to change in the kinetic energy of that object. Since the pulley is at rest initially, initial kinetic energy is equal to zero.
Since the applied force is constant, it is easy to find the work done on the pulley. If the force wouldn’t be constant, we have to integrate the force over the distance travelled.
The speed of the string after it has unwound 1.25 m is ; 2.35 m/s
Given data :
moment of inertia ( I ) = 0.0352 kgm²
Radius of pulley ( r ) = 12.5 cm = 0.125 m
Force  ( F ) = 5 N
distance travelled by the string = 1.25 m
Applying the work energy theorem ( Wtotal = ΔK )  which states that the total work done in an object is equal to the change in kinetic energy within the object.
Using the equation below
Speed of string ( v ) = w * r
first step : determine the value of w
Fx = 1/2 Iw² - 0
5 * 1.25  = 1/2 * ( 0.0352 ) * w²
solve for w
therefore : w = 18.84 rad/s
Next step : determine the speed of the spring
v = w * r
 = 18.84 * 0.125
 = 2.35 m/s
Hence we can conclude that The speed of the string after it has unwound 1.25 m is ; 2.35 m/s.
Learn more about work energy theorem : https://brainly.com/question/14279135
