Answer:
t = 8.391s
Explanation:
we know that:
T = Iα
where T is the torque, I the moment of inertia and α the angular aceleration. So:
Fr-[tex]T_k[/tex] = Iα
where F is the tension of hose, r the radius and [tex]T_k[/tex] is the torque exerts by the friction.
Then, replacing the data:
(29N)(0.17m)-(3.5n*m)=(0.57kg*m^2)α
solving for α:
α = 2.508 rad/s^2
we also know that:
a = αr
where a is the linear aceleration, so:
a = 2.508rad/s*0.17m
a = 0.426 m/s^2
Finally:
x = [tex]\frac{1}{2}at^2[/tex]
where x is the large of the hose, a the linear aceleration and t the time. Replacing values:
15m = [tex]\frac{1}{2}(0.426)t^2[/tex]
Solving for t:
t = 8.391s
