A 18.0-m length of hose is wound around a reel, which is initially at rest. The
ID: 1261095 • Letter: A
Question
A 18.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.400 kgm2, and its radius is 0.200 m. When turning, friction at the axle exerts a torque of magnitude 3.40 Nm on the reel. If the hose is pulled so that the tension in it remains a constant 26.0 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping.
A 18.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.400 kg.m2, and its radius is 0.200 m. When turning, friction at the axle exerts a torque of magnitude 3.40 N.m on the reel. If the hose is pulled so that the tension in it remains a constant 26.0 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping.Explanation / Answer
Length of the hose is L = 18.0 m
radius r = 0.200m
moment of inertia I = 0.400 kg m^2
circumference = 2?r
= 2? * 0.200 m
= 1.2566 m
Total angle of rotation is 18.0 m / 1.2566 * 2?
= 90 rad
torque = moment of inertia * angular acceleration
3.40 N m = 0.400 kg m^ 2 * ?
? = 8.5 rad /s^2
w = w_0t +1/2 ? t^2
90 rad = 0 + 1/2 * ( 8.5 ) * t^2
t = 4.602 s
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.