Question

Analysis Model Tutorial A4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 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 2.30 m/s? (a) How much work has been done on the spool when it reaches an angular speed of 4.00 rad/s? (b) How long does it take the spool to reach this angular speed? (c) How much cord is left on the spool when it reaches this angular speed? Part 1 of 13 - Conceptualize: To simulate this situation, try pulling toilet paper off a roll with an acceleration of your hand. You will probably end up with a huge mess! Try pulling fishing line off a reel or wire off a spool from the electronics store. (Buy it first and take it home; don't do this with the merchant's merchandise in the store!) Imagine that someone's hand pulls on the cord in the problem, so that the hand moves with the acceleration of 2.30 m/s2. Let's use the notations for the radius of the spool, m for its mass, a for the acceleration of the cord, and wp for the final angular speed of the spool. We'll call the initial length of cord wrapped on the spool t. Part 2 of 13 - Categorize: (1) Identify The spool and light cord as a system. Which analysis model below correctly describes the system as the cord is pulled and will be most useful for solving part (ə) of this problem? Origid object under constant angular acceleration solated system (energy) Ononisolated system (energy) Origid object under a net torque O none of the above Submit Continue

Answer 1

L = 4.0m Work done = W = £ I (wy - with) I= 2mp2 n=1kg, r=a5m, a = 2.3 m/s, wino, a= a 2 = 2 3 2 = 4.6 radish wizo wf = 4.0 rad's (a) W- $***1*60-53*[w?com] wz 1x0:25x+6 = 1.0J (6) Wp = Witat t = 1 = 0.878 4=0+ 4.6*t 4.6 (0) s=x0 8 = Wat that² 8 = 0 +4x4.6 xlO:9733 S = 2.3 *0.87 x 0.5 s= 0.87 m