Radius Nylon
How much work has been done on the spool, when it reaches an angular speed of 9.29 rad/s? Answer in units of J
A 1.66 m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.416 m and mass 1.03 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 1.45 m/s^2.
How much work has been done on the spool, when it reaches an angular speed of 9.29 rad/s? Answer in units of J.
Assuming there is enough cord on the spool, how long does it take the spool to reach this angular speed? Answer in units of s.
Ok, first we need to find the tension of the cord :
Using rotational dynamics :
Tension = T
T*R = I*alpha
alpha = a / R
a = linear acceleration
T*0.416 = I*alpha
I = moment of inertia = M*R^2
T*0.416 = 1.03*(0.416)^2*(1.45 / 0.416)
T = 1.5 Newtons
To find the work done by the cord on the spool :
We need to find the angle theta, made by the cylinder :
Wo = 0 rad/s
Wf = 9.29 rad / s
alpha = 3.48 rad/s^2
9.29^2 = 2*3.48*theta
theta = 12.4 (rad)
Work = 1.5*(12.4*0.416)
Work = 7.74 Joules
Hope that helps
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