Starting from rest, a constant force F=100N is applied to the free end of a 50-m cable wrapped around the outer rim of a uniform solid cylinder. The cylinder has mass 4.00 kg and diameter 30.0 cm and is free to turn about a fixed, frictionless axle through its center. (a) How long does it take to unwrap all the cable, and (b) how fast is the cable moving just as the last bit comes off?

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter39: Relativity
Section: Chapter Questions
Problem 1PQ
icon
Related questions
Question

Starting from rest, a constant force F=100N is applied to the free end of a 50-m cable wrapped around the outer rim of a uniform solid cylinder. The cylinder has mass 4.00 kg and diameter 30.0 cm and is free to turn about a fixed, frictionless axle through its center.

(a) How long does it take to unwrap all the cable, and

(b) how fast is the cable moving just as the last bit comes off?

 

the answer should be the one in the picture but i need a more detailed solution please help

dran
EXECUTE: (a) Er, = 1a, and a = Ra gives ÷MR²( "m.
= Ra gives FR=MR'a = Mr² "
2F 200 N
= 50 m/s². Distance the cable moves: x – xo = Vox! + zat²
Atan
M 4.00 kg
1
gives 50 m =-(50 m/s²)t² and t=1.41 s. v, =Vox + a,t = 0 + (50 m/s² )(1.41 s) = 70.5 m/s.
Transcribed Image Text:dran EXECUTE: (a) Er, = 1a, and a = Ra gives ÷MR²( "m. = Ra gives FR=MR'a = Mr² " 2F 200 N = 50 m/s². Distance the cable moves: x – xo = Vox! + zat² Atan M 4.00 kg 1 gives 50 m =-(50 m/s²)t² and t=1.41 s. v, =Vox + a,t = 0 + (50 m/s² )(1.41 s) = 70.5 m/s.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Torque
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations…
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
Physics
ISBN:
9780534408961
Author:
Stephen T. Thornton, Jerry B. Marion
Publisher:
Cengage Learning