Physics for Scientists and Engineers, Vol. 1
Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
bartleby

Videos

Question
Book Icon
Chapter 6, Problem 64P

(a)

To determine

The work done by the force acting on the particle and the velocity of the particle.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The force acting on the particle is (2.0N/m2)x2i^ . The particle moves along a straight line from point (2.0m,2.0m) topoint (2.0m,7.0m) . The particle starts moving from rest.

Formula used:

Write the expression of work done by a particle.

  W=x1x2F.ds   ........ (1)

Here, W is the work done, F is the force acting on the particle, x1 is the initial position of the particle and x2 is the final position of the particle.

Write the expression for the work-energy theorem.

  W=KfKi   ........ (2)

Here, W is the work done, Kf is the final kinetic energy of the particle and Ki is the initial kinetic energy of the particle.

Calculation:

Write the expression for the displacement of the particle.

  ds=(x2x1)i^+(y2y1)j^

Here, ds is the magnitude of displacement, (x1,y1) are the initial position coordinates of the particle and (x2,y2) are the final position coordinates of the particle.

Substitute 0m for (x2x1) and 5m for (y2y1) in the above expression.

  ds=5j^

Substitute (2.0N/m2)x2i^ for F , 5j^ for dx , 2 for x1 and 7 for x2 inexpression (1).

  W=27((2.0N/m2)x2i^).(5j^)=0

Write the expression for the kinetic energy of the particle.

  K=12mv2

Here, k is the kinetic energy, m is the mass of the particle and v is the velocity of the particle.

Write the expression of the final kinetic energy of the particle.

  Kf=12mvf2   ........ (3)

Here, vf is the final velocity of the particle and Kf is the final kinetic energy.

Substitute 12mvf2 for Kf , 0 for Ki and 0 for W in expression (2).

  0=12mvf20

Rearrange the above expression.

  vf=0

Conclusion:

Thus, the work done is 0 and the final speed of the particle is 0.

(b)

To determine

The work done by the force acting on the particle and the velocity of the particle.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The particle moves along a straight line from point (2.0m,2.0m) to point (5.0m,6.0m) .

Calculation:

Write the expression for the displacement of the particle.

  ds=(dx)i^+(dy)j^

Here, dx is the magnitude of displacement, dx is the displacement of the particle along x axis and dy is the displacement of the particle along y axis.

Substitute (2.0N/m2)x2i^ for F , (dx1i^+dy1j^) for dx , 2 for x1 and 5 for x2 inexpression (1).

  W=25((2.0N/m2)x2i^).(dxi^+dyj^)=(2.0N/m2)25x2dx=(2.0N/m2)[x33]25=78J

Substitute 12mvf2 for Kf , 0 for Ki and 78J for W in expression (2).

  78J=12mvf20

Rearrange the above expression.

  vf=2(78J)m=156Jm

Here, m is the mass of the particle.

Conclusion:

Thus, the work done is 78J and the final speed of the particle is 156Jm .

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
The particle in is in equilibrium and F4 = 165 lb. Part A Determine the magnitude of F1. Express your answer in pounds to three significant figures. ΑΣΦ tvec F₁ = Submit Request Answer Part B Determine the magnitude of F2. Express your answer in pounds to three significant figures. ΑΣΦ It vec F2 = Submit Request Answer Part C Determine the magnitude of F3. Express your answer in pounds to three significant figures. ? ? lb lb F₂ 225 lb 135° 45° 30° -60°-
The 10-lb weight is supported by the cord AC and roller and by the spring that has a stiffness of k = 10 lb/in. and an unstretched length of 12 in. as shown in. Part A Determine the distance d to maintain equilibrium. Express your answer in inches to three significant figures. 節 ΕΠΙ ΑΣΦ d = *k J vec 5 t 0 ? d C A in. 12 in. B
The members of a truss are connected to the gusset plate as shown in . The forces are concurrent at point O. Take = 90° and T₁ = 7.5 kN. Part A Determine the magnitude of F for equilibrium. Express your answer to three significant figures and include the appropriate units. F = Value Submit Request Answer Part B 0 ? Units Determine the magnitude of T2 for equilibrium. Express your answer to three significant figures and include the appropriate units. ? T₂ = Value Units T₁ C
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
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
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
Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY