a colic Now let's use conservation of energy to calculate the kinetic energy of a rotating cylinder. Specifically, we will employ the work-energy theorem to relate the work done on the cylinder to the change in its rotational kinetic energy. A light, flexible, nonstretching cable is wrapped energy several times around a winch drum-a solid cylinder with mass 50 kg and diameter 0.14 m that rotates about a stationary horizontal axis turning on frictionless bearings we cany (Figure 1). The free end of the cable is pulled with a constant force of magnitude 9.7 N for a distance of 2.0 m. It unwinds without slipping, turning the cylinder as it does so. If the cylinder is initially at rest, find its final angular velocity w and the final speed of the cable. on frictions Figure F 2.0 m 50 kg 1 of 2> D cylinder to determine its moment of inertia. The work done on the cylinder by the force is W = Fs (9.7N) (2.0m) = 19J The moment of inertia for a solid cylinder is The work-energy theorem (W = AK) then gives I = MR² = (50kg) (7.0 × 10-²m)² = 0.12kg. m² Part A - Practice Problem: 19J 18rad/s The final speed of the cable is equal to the final tangential speed, Utan, of the cylinder. HA = Utan = Rw = (7.0 × 10-2m) (18rad/s) = 1.2m/s REFLECT The speed of the cable at each instant equals the tangential component of velocity of the cylinder because there is no slipping between cable and cylinder; if there were slipping, the winch wouldn't work. wwww. (0.12kg-m²)w² = Suppose we replace the solid cylinder with a thin-walled cylinder having the same mass and radius. How does the final speed of the cable differ from our result for the solid cylinder? Express your answer to two significant figures and include appropriate units. ?
a colic Now let's use conservation of energy to calculate the kinetic energy of a rotating cylinder. Specifically, we will employ the work-energy theorem to relate the work done on the cylinder to the change in its rotational kinetic energy. A light, flexible, nonstretching cable is wrapped energy several times around a winch drum-a solid cylinder with mass 50 kg and diameter 0.14 m that rotates about a stationary horizontal axis turning on frictionless bearings we cany (Figure 1). The free end of the cable is pulled with a constant force of magnitude 9.7 N for a distance of 2.0 m. It unwinds without slipping, turning the cylinder as it does so. If the cylinder is initially at rest, find its final angular velocity w and the final speed of the cable. on frictions Figure F 2.0 m 50 kg 1 of 2> D cylinder to determine its moment of inertia. The work done on the cylinder by the force is W = Fs (9.7N) (2.0m) = 19J The moment of inertia for a solid cylinder is The work-energy theorem (W = AK) then gives I = MR² = (50kg) (7.0 × 10-²m)² = 0.12kg. m² Part A - Practice Problem: 19J 18rad/s The final speed of the cable is equal to the final tangential speed, Utan, of the cylinder. HA = Utan = Rw = (7.0 × 10-2m) (18rad/s) = 1.2m/s REFLECT The speed of the cable at each instant equals the tangential component of velocity of the cylinder because there is no slipping between cable and cylinder; if there were slipping, the winch wouldn't work. wwww. (0.12kg-m²)w² = Suppose we replace the solid cylinder with a thin-walled cylinder having the same mass and radius. How does the final speed of the cable differ from our result for the solid cylinder? Express your answer to two significant figures and include appropriate units. ?
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter11: Angular Momentum
Section: Chapter Questions
Problem 54P: A cylinder with rotational inertia I1=2.0kgm2 rotates clockwise about a vertical axis through its...
Related questions
Question
Transcribed Image Text:Now let's use conservation of energy to calculate the
kinetic energy of a rotating cylinder. Specifically, we will
employ the work-energy theorem to relate the work done
on the cylinder to the change in its rotational kinetic
energy. A light, flexible, nonstretching cable is wrapped
several times around a winch drum-a solid cylinder with
mass 50 kg and diameter 0.14 m that rotates about a
stationary horizontal axis turning on frictionless bearings
(Figure 1). The free end of the cable is pulled with a
constant force of magnitude 9.7 N for a distance of 2.0
m. It unwinds without slipping, turning the cylinder as it
does so. If the cylinder is initially at rest, find its final
angular velocity w and the final speed v of the cable.
Figure
F
2.0 m
50 kg
1 of 2
SET UP (Figure 2) shows our sketch for this problem.
SOLVE No energy is lost due to friction, so the final kinetic energy K = Iw² of the cylinder is equal to the work W = F's done by the
force (of magnitude F, pulling through a distance s parallel to the force) acting on the cylinder. We need to use the mass and diameter of the
cylinder to determine its moment of inertia. The work done on the cylinder by the force is
W = Fs = = (9.7N) (2.0m) =
= 19J
The moment of inertia for a solid cylinder is
The work-energy theorem (W = AK) then gives
I = MR² = (50kg) (7.0 × 10-²m)² = 0.12kg. m²
Part A Practice Problem:
19J
18rad/s
The final speed of the cable is equal to the final tangential speed, Utan, of the cylinder.
Utan =
HA
=
W
(0.12kg-m²)w²
=
REFLECT The speed of the cable at each instant equals the tangential component of velocity of the cylinder because there is no slipping
between cable and cylinder; if there were slipping, the winch wouldn't work.
I ?
Rw = (7.0 x 10-2m) (18rad/s) = 1.2m/s
Suppose we replace the solid cylinder with a thin-walled cylinder having the same mass and radius. How does the final speed of the cable
differ from our result for the solid cylinder?
Express your answer to two significant figures and include appropriate units.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Knowledge Booster
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.Recommended textbooks for you
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College