Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A pulley wheel that is $8.0 cm$ in diameter has a $5.6 m$ long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of $1.5 rad / s^{2}$ . (a) Through what angle must the wheel turn for the cord to unwind completely? (b) How long will this take?

a) The angle that the wheel must turn for the cord to unwind completely is . $140 rad$

b) Time taken by wheel to turn for the cord to unwind completelyis. $14 sec$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

i) Diameter of pulley is $D = 8.0 cm$ ,

ii) Length of cord is $L = 5.6 m$ ,

iii) Angular acceleration is $α = 1.5 rad / s^{2}$ ,

Step 2: Determining the concept

Find the circumference of the wheel. Using circumference and length of cord, find the number of revolutions. Find the angle using the revolutions. Then, use rotational kinematic equations to find the time.

The circumference of the pulley,

$c = πd$

The number of revolutions made,

$θ = 2 πn$

Total angular distance travelled,

$θ = 2 πn$

Relation between angular distance and time taken,

$θ = ω_{0} t + \frac{1}{2} {αt}^{2}$

where, Iisthe moment of inertia, M, m are masses, r is radius, t is time taken.

Step 3: (a) Determining the angle must the wheel turn for the cord to unwind completely

Circumference of wheel is c,

$c = π d$

$c = π \times 0.08 m$

$c = 0.25 m$

Now, number of revolutions n as follows:

$n = \frac{Length of cord}{circumference of wheel}$

$n = \frac{5.6 m}{0.25 m}$

$n = 22.3 revolutions$

Now, angle is as follows:

$θ = 2 π n$

$θ = 2 π \times 22.3$

$θ = 140 rad$

Hence,the angle that the wheel must turn for the cord to unwind completely is $140 rad$ .

Step 4: (b) Determining how long wheel turn for the cord to unwind completely

Now, time can be calculated using the equation-

$θ = ω_{0} \times t + \frac{1}{2} α t^{2}$

$140 rad = 0 \times t + \frac{1}{2} \times 1.5 m / s^{2} \times t^{2}$

$t = 13.7 sec$

In two significant figures,

$t = 14 s$

Hence, time taken by wheel to turn for the cord to unwind completelyis $14 sec$ .

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

A pulley wheel that is $8.0 cm$ in diameter has a $5.6 m$ long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of $1.5 rad / s^{2}$ . (a) Through what angle must the wheel turn for the cord to unwind completely? (b) How long will this take?

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the angle must the wheel turn for the cord to unwind completely

Step 4: (b) Determining how long wheel turn for the cord to unwind completely

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

A pulley wheel that is 8.0 cm in diameter has a 5.6 m long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 1.5 rad/s2 . (a) Through what angle must the wheel turn for the cord to unwind completely? (b) How long will this take?

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the angle must the wheel turn for the cord to unwind completely

Step 4: (b) Determining how long wheel turn for the cord to unwind completely

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

A pulley wheel that is $8.0 cm$ in diameter has a $5.6 m$ long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of $1.5 rad / s^{2}$ . (a) Through what angle must the wheel turn for the cord to unwind completely? (b) How long will this take?