Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
bartleby

Concept explainers

bartleby

Videos

Question
100%
Book Icon
Chapter 5, Problem 36P

(a)

To determine

To Evaluate: The distance the boy from the dock when he reaches the bow.

(a)

Expert Solution
Check Mark

Answer to Problem 36P

3.6 m

Explanation of Solution

Given:

Mass of boy is 60 kg .

Mass of canoe is 40 kg .

Distance between the boy and bow of canoe is 6.0 m .

Center of canoe is 3.0 m from the bow.

Formula used:

The x -coordinate position of center of mass can be calculated by the following formula:

  Xcm=(xbmb+xcmc)(mb+mc)

Here xb and xc are the distances of boy from bow and distance of center of canoe from bow respectively, while mb and mc are the masses of boy and canoe respectively.

Calculation:

The x -coordinate for the center of mass is calculated as follows:

  Xcm=(xbmb+xcmc)(mb+mc)

Substituting mb=60 kg, xb=6.0 m, mc=40 kg and xc=3.0 m

  Xcm=(6.0 m×60.0 kg)+(3.0 m×40.0 kg)(60.0 kg + 40.0 kg)      = 4.8 m

Now assuming that the boy moves by a distance of x , then the distance of bow from the center of canoe can be given by the following formula:

  xc ' =3.0 m+x

as the boy moves towards the bow, the center of mass of the system would be as follows:

  Xcm=(xbmb+xcmc)(mb+mc)

Substituting: Xcm=4.8 m, mb=60.0 kg, mc=40.0 kg, x=xb and xc=(3.0 m+x)

  4.8 m=(x×60.0 kg)+(3.0 m+x)×40.0 kg(60.0 kg+40.0 kg)480 kgm=x(60.0 kg)+(3.0 m+x)40.0 kgx  =480 kgm120 kgm100 kg     = 3.6 m

Conclusion:

As the boy moves towards the bow, the distance between the boy and dock is 3.6 m.

(b)

To determine

Whether the canoe is moving or not.

(b)

Expert Solution
Check Mark

Explanation of Solution

Introduction:

The x-coordinate position of center of mass can be calculated by the following formula:

  Xcm=(xbmb+xcmc)(mb+mc)

Here xb and xc are the distances of boy from bow and distance of center of canoe from bow respectively, while mb and mc are the masses of boy and canoe respectively.

It has been shown that there is no external force acting on the system, and no friction between water and canoe. Hence, the canoe does not move, since the system’s position of center of mass does not change.

The coordinate for center of mass is calculated as follows:

  Xcm=(xbmb+xcmc)(mb+mc)

Substituting mb=60 Kg, xb=6.0 m, mc=40 Kg and xc=3.0 m

  Xcm=(6.0 m×60.0 kg)+(3.0 m×40.0 kg)(60.0 kg + 40.0 kg)      = 4.8 m

As the center of mass of the system remains the same, the canoe does not move under the given conditions.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
81 SSM Figure 29-84 shows a cross section of an infinite conducting sheet carrying a current per unit x-length of 2; the current emerges perpendicularly out of the page. (a) Use the Biot-Savart law and symmetry to show that for all points B P P. BD P' Figure 29-84 Problem 81. x P above the sheet and all points P' below it, the magnetic field B is parallel to the sheet and directed as shown. (b) Use Ampere's law to prove that B = ½µλ at all points P and P'.
What All equations of Ountum physics?
Please rewrite the rules of Quantum mechanics?
Knowledge Booster
Background pattern image
Physics
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
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Text book image
An Introduction to Physical Science
Physics
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:Cengage Learning
Newton's Second Law of Motion: F = ma; Author: Professor Dave explains;https://www.youtube.com/watch?v=xzA6IBWUEDE;License: Standard YouTube License, CC-BY