Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3, Problem 6Q
If →V=→V1+→V2 , is V necessarily greater than V1, and/or V2? Discuss.
Expert Solution & Answer
Solution
To Determine:
Whether the magnitude of the sum of two vectors is necessarily greater than the magnitude of V1 and/or V2.
Solution:
No, the magnitude of the sum of two vectors is not necessarily greater than the magnitude of V1 and/or V2 .
Explanation:
The sum of the vector could result in a shorter vector than the original ones, therefore the magnitude would be less than the other vectors. The resultant magnitude depends on the direction in which the two vectors are inclined.
→V=→V1+→V2
The resultant magnitude of vector can be obtained by:
V=√V12+V22+2V1V2cosθ
Here, the maximum value of cosθ could be 1 and minimum value could be -1.
If cosθ =1
V=√V12+V22+2V1V2V=√(V1+V2)2V=(V1+V2)
This implies that the value of V is greater than the value of each V1 and V2 . If cosθ =−1
V=√V12+V22−2V1V2V=√(V1−V2)2V=(V1−V2)
This implies that the value of V is less than the value of each V1 and V2 .
Conclusions:
The magnitude of the sum of the vectors could be greater than the magnitude of any of the vectors, but not always.
Chapter 3 Solutions
Physics: Principles with Applications
Ch. 3 - One car travels due east at 40 km/h, and a second...Ch. 3 - Can you conclude that a car is not accelerating if...Ch. 3 - Give several examples of an object's motion in...Ch. 3 - Can the displacement vector for a particle moving...Ch. 3 - During baseball practice, a player hits a very...Ch. 3 - If V =V 1+V 2 , is V necessarily greater than V1,...Ch. 3 - Two vectors have length V1=3.5km and V2=4.0km ....Ch. 3 - Can the magnitude of a vector ever (a) equal, or...Ch. 3 - Prob. 9QCh. 3 - How could you determine the speed a slingshot...
Ch. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - A projectile is launched at an upward angle of 300...Ch. 3 - Prob. 15QCh. 3 - Two cannonballs, A and B, are fired from the...Ch. 3 - 18. A person sitting in an enclosed train car,...Ch. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - A car is driven 225 km west and then 98 km...Ch. 3 - A delivery truck travels 21 blocks north, 16...Ch. 3 - If Vx=9.80 units and Vy=6.40 units, determine the...Ch. 3 - Graphically determine the resultant of the...Ch. 3 - V is a vector 24.8 units in magnitude and points...Ch. 3 - Vector V is 6.6 using long and points along the...Ch. 3 - Figure 3-33 shows two vectors, A and B , whose...Ch. 3 - Prob. 8PCh. 3 - Three vectors are shown in Fig. 3-35 Q. Their...Ch. 3 - (a) given the vectors A and B shown in Fig. 3-35,...Ch. 3 - Determine the vector AC , given the vectors A and...Ch. 3 - For the vectors shown in Fig. 3—35, determine (a)...Ch. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - 17. (l) A tiger leaps horizontally from a...Ch. 3 - 18. (l) A diver running 2.5 m/s dives out...Ch. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Prob. 53GPCh. 3 - Prob. 54GPCh. 3 - Prob. 55GPCh. 3 - Prob. 56GPCh. 3 - Prob. 57GPCh. 3 - Prob. 58GPCh. 3 - Prob. 59GPCh. 3 - Prob. 60GPCh. 3 - Prob. 61GPCh. 3 - Prob. 62GPCh. 3 - Prob. 63GPCh. 3 - Prob. 64GPCh. 3 - Prob. 65GPCh. 3 - Prob. 66GPCh. 3 - Prob. 67GPCh. 3 - Prob. 68GPCh. 3 - Prob. 69GPCh. 3 - Prob. 70GPCh. 3 - Prob. 71GPCh. 3 - Prob. 72GPCh. 3 - Prob. 73GPCh. 3 - Prob. 74GPCh. 3 - Prob. 75GP
Additional Science Textbook Solutions
Find more solutions based on key concepts
If all of Earths nitrogen-fixing prokaryotes were to die suddenly, what would happen to the concentration of ni...
Biology: Life on Earth with Physiology (11th Edition)
The following data were obtained from a disk-diffusion test. Antibiotic Zone of Inhibition A 15 mm B 0 mm c 7 m...
Microbiology: An Introduction
15.1 What purpose do the bla and lacZ genes serve in the plasmid vector ?
Genetic Analysis: An Integrated Approach (3rd Edition)
5. When the phenotype of heterozygotes is intermediate between the phenotypes of the two homozygotes, this patt...
Biology: Life on Earth (11th Edition)
Which of the following factors would tend to increase membrane fluidity? A. a greater proportion of unsaturated...
Campbell Biology in Focus (2nd Edition)
1. In uniform circular motion, which of the following are constant: speed, velocity, angular velocity, centripe...
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Knowledge Booster
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
- Can someone helparrow_forwardCan someone help mearrow_forward3. Four identical small masses are connected in a flat perfect square. Rank the relative rotational inertias (IA, IB, IC) about the three axes of rotation shown. Axes A and B are in the plane of the square, and axis C is perpendicular to the plane, through mass m1. ΙΑ IB m2 m1 m3 Ic m4 (a) IAarrow_forward
- Consider the circuit shown in the figure below. (Assume L = 5.20 m and R2 = 440 Ω.) (a) When the switch is in position a, for what value of R1 will the circuit have a time constant of 15.4 µs? (b) What is the current in the inductor at the instant the switch is thrown to position b?arrow_forwardCan someone helparrow_forwardCan someone help mearrow_forward
- A particle in a box between x=0 and x=6 has the wavefunction Psi(x)=A sin(2πx). How muchenergy is required for the electron to make a transition to Psi(x)= A’ sin(7π x/3). Draw anapproximate graph for the wavefunction. Find A and A'arrow_forwardA proton is moving with 10^8 m/s speed. Find the De Broglie wavelength associated with theproton and the frequency of that wave.arrow_forwardFind the wavelength of the photon if a (Li--) electron makes a transition from n=4 to n=3. Findthe Bohr radius for each state.arrow_forward
- A photon with wavelength 3000 nm hits a stationary electron. After the collision electron isscattered to 60 degrees. Find the wavelength and frequency of the scattered photon.arrow_forwardA metal has threshold frequency 10^15. Calculate the maximum kinetic energy of the ejectedelectron if a laser beam with wavelength 1.5 10^-7 m is projected on the metal.arrow_forwardDetermine the direction of the vector V, B, or ♬ that is missing from the pair of vectors shown in each scenario. Here, u is the velocity vector of a moving positive charge, B is a constant and uniform magnetic field, and F is the resulting force on the moving charge. 1. 2. 3. B OB F 4. ↑F F 5. 怔 ↑ ↑F Answer Bank 6. ↑ TE Farrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Introduction to Vectors and Their Operations; Author: Professor Dave Explains;https://www.youtube.com/watch?v=KBSCMTYaH1s;License: Standard YouTube License, CC-BY