Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
bartleby

Videos

Question
Book Icon
Chapter 5, Problem 118P

(a)

To determine

The acceleration of center of mass of two block cylinder string system.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The mass of cylinder is mc .

Formula used:

Write expression for total force on the system.

  Fcm=F1+F2+Fc

Substitute Macm for Fcm , m1a1 for F1 , m2a2 for F2 and mcac for Fc .

  Macm=m1a1+m2a2+mcac

Substitute m1+m2+m3 for M , a for a1 , a for a2 and 0 for a3 in above expression.

  acm=a(m1m2m1+m2+m3)  .......(1)

Calculation:

Draw free body diagram of blocks of Atwood’s machine.

  Physics for Scientists and Engineers, Chapter 5, Problem 118P , additional homework tip  1

Write expression for net force in block of mass m2 .

  F2=0

Substitute Tm2gm2a2 for F2 in above expression.

  Tm2gm2a2=0  .......(2)

Write expression for net force in block of mass m1 .

  F1=0

Substitute m1gTm1a1 for F1 in above expression.

  m1gTm1a1=0

Rearrange above expression for T .

  T=m1a1m1g

Substitute m1a1m1g for T in equation (2).

  m1a1m1gm2gm2a2=0

Substitute a for a1 and a for a2 in above expression and solve for a .

  a=m1m2m1+m2g

Substitute m1m2m1+m2g for a in equation (1).

  acm=( m 1 m 2 m 1 + m 2 g)( m 1 m 2 m 1 + m 2 + m 3 )acm= ( m 1 m 2 )2( m 1 + m 2 )( m 1 + m 2 + m 3 )g

Conclusion:

Thus, the acceleration of COM is ( m 1 m 2 )2(m1+m2)(m1+m2+m3)g .

(b)

To determine

The force exerted by the support.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The mass of cylinder is mc .

Formula used:

Write expression for total force on the system.

  Fcm=F1+F2+Fc

Substitute Macm for Fcm , m1a1 for F1 , m2a2 for F2 and mcac for Fc .

  Macm=m1a1+m2a2+mcac

Substitute m1+m2+m3 for M , a for a1 , a for a2 and 0 for a3 in above expression.

  acm=a(m1m2m1+m2+m3)  .......(1)

Write expression for force exerted by the support.

  F=MgMacm  .......(2)

Calculation:

Draw free body diagram of blocks of Atwood’s machine.

  Physics for Scientists and Engineers, Chapter 5, Problem 118P , additional homework tip  2

Write expression for net force in block of mass m2 .

  F2=0

Substitute Tm2gm2a2 for F2 in above expression.

  Tm2gm2a2=0  .......(3)

Write expression for net force in block of mass m1 .

  F1=0

Substitute m1gTm1a1 for F1 in above expression.

  m1gTm1a1=0

Rearrange above expression for T .

  T=m1a1m1g

Substitute m1a1m1g for T in equation (3).

  m1a1m1gm2gm2a2=0

Substitute a for a1 and a for a2 in above expression and solve for a .

  a=m1m2m1+m2g

Substitute m1m2m1+m2g for a in equation (1).

  acm=( m 1 m 2 m 1 + m 2 g)( m 1 m 2 m 1 + m 2 + m 3 )acm= ( m 1 m 2 )2( m 1 + m 2 )( m 1 + m 2 + m 3 )g

Substitute ( m 1 m 2 )2(m1+m2)(m1+m2+m3)g for acm .

  F=MgM( ( m 1 m 2 )2( m 1 + m 2 )( m 1 + m 2 + m 3 )g)

Substitute m1+m2+m3 for M in above expression and solve.

  F=(4m1m2m1+m2+mc)g

Conclusion:

Thus, force exerted by the support is (4m1m2m1+m2+mc)g .

(c)

To determine

Tension T in the string; to show that F=mcg+2T .

(c)

Expert Solution
Check Mark

Explanation of Solution

Given:

Formula used:

Write expression for total force on the system.

  Fcm=F1+F2+Fc

Substitute Macm for Fcm , m1a1 for F1 , m2a2 for F2 and mcac for Fc .

  Macm=m1a1+m2a2+mcac

Substitute m1+m2+m3 for M , a for a1 , a for a2 and 0 for a3 in above expression.

  acm=a(m1m2m1+m2+m3)  .......(1)

Write expression for force exerted by the support.

  F=MgMacm  .......(2)

Draw free body diagram of blocks of Atwood’s machine.

  Physics for Scientists and Engineers, Chapter 5, Problem 118P , additional homework tip  3

Write expression for net force in block of mass m2 .

  F2=0

Substitute Tm2gm2a2 for F2 in above expression.

  Tm2gm2a2=0  .......(3)

Write expression for net force in block of mass m1 .

  F1=0

Substitute m1gTm1a1 for F1 in above expression.

  m1gTm1a1=0

Rearrange above expression for T .

  T=m1a1m1g  .......(4)

Substitute m1a1m1g for T in equation (3).

  m1a1m1gm2gm2a2=0

Substitute a for a1 and a for a2 in above expression and solve for a .

  a=m1m2m1+m2g

Substitute m1m2m1+m2g for a1 in equation (4) and solve for T .

  T=2m1m2gm1+m2

Calculation:

Substitute m1m2m1+m2g for a in equation (1).

  acm=( m 1 m 2 m 1 + m 2 g)( m 1 m 2 m 1 + m 2 + m 3 )acm= ( m 1 m 2 )2( m 1 + m 2 )( m 1 + m 2 + m 3 )g

Substitute ( m 1 m 2 )2(m1+m2)(m1+m2+m3)g for acm .

  F=MgM( ( m 1 m 2 )2( m 1 + m 2 )( m 1 + m 2 + m 3 )g)

Substitute m1+m2+m3 for M in above expression and solve.

  F=4m1m2m1+m2g+mcg

Substitute T for 2m1m2gm1+m2 in above expression.

  F=2T+mcg

Conclusion:

Thus, the tension in the string is 2m1m2gm1+m2 .

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
You have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. It is to be constructed in the shape of a hollow ring of mass 58,500 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 125 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…
The polar ice caps have a combined mass of about 2.65 × 1019 kg. If all of the ice in the polar ice caps melted, by how much time would the length of a day (Earth's rotational period) change? For simplicity, assume each ice cap is an identical thin solid disk with a radius of 7.20 x 105 m. Find the change both in seconds and as a percentage of duration of a day. change in time percent change (No Response) s (No Response) %
. A space probe in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope is I = 17.5 kg m² about the axis of the gyroscope, and the moment of inertia of the rest of the space probe is I = 5.00 × 105 kg • m² about the same axis. Initially both the space probe and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 110 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the space probe's orientation by 24.0°? (No Response) s

Chapter 5 Solutions

Physics for Scientists and Engineers

Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - Prob. 42PCh. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 65PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - Prob. 76PCh. 5 - Prob. 77PCh. 5 - Prob. 78PCh. 5 - Prob. 79PCh. 5 - Prob. 80PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - Prob. 84PCh. 5 - Prob. 85PCh. 5 - Prob. 86PCh. 5 - Prob. 87PCh. 5 - Prob. 88PCh. 5 - Prob. 89PCh. 5 - Prob. 90PCh. 5 - Prob. 91PCh. 5 - Prob. 92PCh. 5 - Prob. 93PCh. 5 - Prob. 94PCh. 5 - Prob. 95PCh. 5 - Prob. 96PCh. 5 - Prob. 97PCh. 5 - Prob. 101PCh. 5 - Prob. 102PCh. 5 - Prob. 103PCh. 5 - Prob. 104PCh. 5 - Prob. 105PCh. 5 - Prob. 106PCh. 5 - Prob. 107PCh. 5 - Prob. 108PCh. 5 - Prob. 109PCh. 5 - Prob. 110PCh. 5 - Prob. 111PCh. 5 - Prob. 112PCh. 5 - Prob. 113PCh. 5 - Prob. 114PCh. 5 - Prob. 115PCh. 5 - Prob. 116PCh. 5 - Prob. 117PCh. 5 - Prob. 118PCh. 5 - Prob. 119PCh. 5 - Prob. 120PCh. 5 - Prob. 121PCh. 5 - Prob. 122PCh. 5 - Prob. 123PCh. 5 - Prob. 124PCh. 5 - Prob. 125PCh. 5 - Prob. 126PCh. 5 - Prob. 127PCh. 5 - Prob. 128PCh. 5 - Prob. 129PCh. 5 - Prob. 130PCh. 5 - Prob. 131PCh. 5 - Prob. 132PCh. 5 - Prob. 133PCh. 5 - Prob. 134PCh. 5 - Prob. 135PCh. 5 - Prob. 136PCh. 5 - Prob. 137PCh. 5 - Prob. 138PCh. 5 - Prob. 139P
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
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
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
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Drawing Free-Body Diagrams With Examples; Author: The Physics Classroom;https://www.youtube.com/watch?v=3rZR7FSSidc;License: Standard Youtube License