BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Solutions

Chapter
Section
BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A string is wrapped around a uniform cylinder of mass M and radius R. The cylinder is released from rest with the string vertical and its top end tied to a fixed bar (Fig. P8.90). Show that (a) the tension in the string is one-third the weight of the cylinder, (b) the magnitude of the acceleration of the center of gravity is 2g/3, and (c) the speed  of the center of gravity is (4gh/3)1/2 after the cylinder has descended through distance h. Verify your answer to part (c) with the energy approach.

images

Figure P8.90

(a)

To determine
To verify the tension in the spring is one third of the weight of the cylinder.

Explanation

Given Info:

The mass of the cylinder is M; radius of the cylinder is R , h is the distance from the bar to centre of the cylinder.

The moving cylinder has both translational and rotational motion. Consider downward acceleration as negative.

Figure shows the tension on the string, weight of the cylinder, and direction of acceleration.

Apply translational effect on the cylinder. The cylinder will accelerate with an acceleration a.

From Newton’s second law,

TMg=Ma

  • g is the acceleration due to gravity
  • T is the tension in the string

Consider the inward torque as negative and outward torque as positive.

Formula to calculate torque on the cylinder is,

τ=Iα

  • τ is the torque acting on the cylinder
  • I is the moment of inertia of the cylinder
  • α is the angular acceleration

Negative sign shows the direction on the torque.

Formula to calculate the moment of inertia I is,

I=MR22

Formula to calculate acceleration a in terms of α is,

α=aR

Use a/R for α and MR2/2 for I in τ=Iα to rewrite τ

(b)

To determine
The magnitude of acceleration of the centre of gravity.

(c)

To determine
The magnitude of speed of the centre of gravity.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

What is the abscission zone?

Biology (MindTap Course List)

What are the moral implications of using alcohol during pregnancy?

Understanding Nutrition (MindTap Course List)

An eating pattern with sufficient essential fatty acids includes a. nuts and vegetable oils. b. 1/4 cup of raw ...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What is the difference between a law and a theory?

An Introduction to Physical Science

What does the word apparent mean in apparent visual magnitude?

Horizons: Exploring the Universe (MindTap Course List)

What is physically exchanged during crossing over?

Human Heredity: Principles and Issues (MindTap Course List)

What happens to CO2 in the blood when the kidneys function to control blood pH?

Chemistry for Today: General, Organic, and Biochemistry

A car traveling on a flat (unbanked), circular track accelerates uniformly from rest with a tangential accelera...

Physics for Scientists and Engineers, Technology Update (No access codes included)