Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 10, Problem 26P
To determine
Prove equation 10.26 using the definition of vector product and concept of unit vectors.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine the values of the following unit vector products.
k^⋅k^
ı^×ı^
ı^⋅ȷ^
ȷ^×k^
ı^⋅k^
ı^×k^
I think that I need to be using the Right Hand Rule but I just cant figure it out. Can you please help?
Two vectors A and B are shown in the figure.
The magnitude of their dot product is C, and
the magnitude of their cross product is
1.094 C. Find cos(0).
B
A.
The Vector Product
Two vectors lying in the xy-plane are given by the equations A = 8î + 2j and B = -3î + 3j. Find Ax B and verify that à ×B = -B x A.
SOLUTION
Conceptualize Given the unit-vector notations of the vectors, think about the directions the vectors point in space. Draw them on graph paper and imagine the parallelogram for these vectors.
Categorize Because we use the definition of the cross product discussed in this section, we categorize this example as-Select--
problem.
Write the cross product of the two vectors:
AxB =
î + 2j ) x
î + 3j
Perform the multiplication:
ĀxB = 8î x (-3î) + 8î × 3j +|
j x (-3î) + 2j x
Use the equations for the cross product of unit vectors to evaluate the various terms:
AXB =
To verify that AxB = -B x A, evaluate Bx A:
BxA = (-31 +
Perform the multiplication:
BxA = (-31) x
]î +(-3î) × 2j + 3ĵ × 8î +
j x 2j
Use the equations for the cross product of unit vectors evaluate the various terms:
BxA =
Therefore, Ax B = -B xA
As an alternative method for…
Chapter 10 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 10.1 - A rigid object is rotating in a counterclockwise...Ch. 10.2 - Consider again the pairs of angular positions for...Ch. 10.3 - Ethan and Joseph are riding on a merry-go-round....Ch. 10.4 - Prob. 10.4QQCh. 10.5 - (i) If you are trying to loosen a stubborn screw...Ch. 10.7 - Prob. 10.6QQCh. 10.9 - A solid sphere and a hollow sphere have the same...Ch. 10.10 - A competitive diver leaves the diving board and...Ch. 10.12 - Two items A and B are placed at the top of an...Ch. 10 - A cyclist rides a bicycle with a wheel radius of...
Ch. 10 - Prob. 2OQCh. 10 - Prob. 3OQCh. 10 - Prob. 4OQCh. 10 - Assume a single 300-N force is exerted on a...Ch. 10 - Consider an object on a rotating disk a distance r...Ch. 10 - Answer yes or no to the following questions. (a)...Ch. 10 - Figure OQ10.8 shows a system of four particles...Ch. 10 - As shown in Figure OQ10.9, a cord is wrapped onto...Ch. 10 - Prob. 10OQCh. 10 - Prob. 11OQCh. 10 - A constant net torque is exerted on an object....Ch. 10 - Let us name three perpendicular directions as...Ch. 10 - A rod 7.0 m long is pivoted at a point 2.0 m from...Ch. 10 - Prob. 15OQCh. 10 - A 20.0-kg horizontal plank 4.00 m long rests on...Ch. 10 - (a) What is the angular speed of the second hand...Ch. 10 - Prob. 2CQCh. 10 - Prob. 3CQCh. 10 - Which of the entries in Table 10.2 applies to...Ch. 10 - Prob. 5CQCh. 10 - Prob. 6CQCh. 10 - Prob. 7CQCh. 10 - Prob. 8CQCh. 10 - Three objects of uniform densitya solid sphere, a...Ch. 10 - Prob. 10CQCh. 10 - If the torque acting on a particle about an axis...Ch. 10 - Prob. 12CQCh. 10 - Stars originate as large bodies of slowly rotating...Ch. 10 - Prob. 14CQCh. 10 - Prob. 15CQCh. 10 - Prob. 16CQCh. 10 - Prob. 17CQCh. 10 - During a certain time interval, the angular...Ch. 10 - A bar on a hinge starts from rest and rotates with...Ch. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - The tub of a washer goes into its spin cycle,...Ch. 10 - Why is the following situation impossible?...Ch. 10 - An electric motor rotating a workshop grinding...Ch. 10 - Prob. 8PCh. 10 - Prob. 9PCh. 10 - A wheel 2.00 m in diameter lies in a vertical...Ch. 10 - A disk 8.00 cm in radius rotates at a constant...Ch. 10 - Make an order-of-magnitude estimate of the number...Ch. 10 - A car traveling on a flat (unbanked), circular...Ch. 10 - Prob. 14PCh. 10 - A digital audio compact disc carries data, each...Ch. 10 - Figure P10.16 shows the drive train of a bicycle...Ch. 10 - Big Ben, the Parliament tower clock in London, has...Ch. 10 - Rigid rods of negligible mass lying along the y...Ch. 10 - A war-wolf, or trebuchet, is a device used during...Ch. 10 - Prob. 20PCh. 10 - Review. Consider the system shown in Figure P10.21...Ch. 10 - The fishing pole in Figure P10.22 makes an angle...Ch. 10 - Find the net torque on the wheel in Figure P10.23...Ch. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - A force of F=(2.00i+3.00j) N is applied to an...Ch. 10 - A uniform beam resting on two pivots has a length...Ch. 10 - Prob. 29PCh. 10 - Prob. 30PCh. 10 - Figure P10.31 shows a claw hammer being used to...Ch. 10 - Prob. 32PCh. 10 - A 15.0-m uniform ladder weighing 500 N rests...Ch. 10 - A uniform ladder of length L and mass m1 rests...Ch. 10 - BIO The arm in Figure P10.35 weighs 41.5 N. The...Ch. 10 - A crane of mass m1 = 3 000 kg supports a load of...Ch. 10 - An electric motor turns a flywheel through a drive...Ch. 10 - Prob. 38PCh. 10 - Prob. 39PCh. 10 - In Figure P10.40, the hanging object has a mass of...Ch. 10 - A potters wheela thick stone disk of radius 0.500...Ch. 10 - A model airplane with mass 0.750 kg is tethered to...Ch. 10 - Consider two objects with m1 m2 connected by a...Ch. 10 - Review. An object with a mass of m = 5.10 kg is...Ch. 10 - A playground merry-go-round of radius R = 2.00 m...Ch. 10 - The position vector of a particle of mass 2.00 kg...Ch. 10 - Prob. 48PCh. 10 - Big Ben (Fig. P10.17), the Parliament tower clock...Ch. 10 - A disk with moment of inertia I1 rotates about a...Ch. 10 - Prob. 51PCh. 10 - A space station is constructed in the shape of a...Ch. 10 - Prob. 53PCh. 10 - Why is the following situation impossible? A space...Ch. 10 - The puck in Figure 10.25 has a mass of 0.120 kg....Ch. 10 - A student sits on a freely rotating stool holding...Ch. 10 - Prob. 57PCh. 10 - Prob. 58PCh. 10 - A cylinder of mass 10.0 kg rolls without slipping...Ch. 10 - A uniform solid disk and a uniform hoop are placed...Ch. 10 - A metal can containing condensed mushroom soup has...Ch. 10 - A tennis ball is a hollow sphere with a thin wall....Ch. 10 - Prob. 63PCh. 10 - Review. A mixing beater consists of three thin...Ch. 10 - A long, uniform rod of length L and mass M is...Ch. 10 - The hour hand and the minute hand of Big Ben, the...Ch. 10 - Two astronauts (Fig. P10.67), each having a mass...Ch. 10 - Two astronauts (Fig. P10.67), each having a mass...Ch. 10 - Prob. 69PCh. 10 - Prob. 70PCh. 10 - The reel shown in Figure P10.71 has radius R and...Ch. 10 - Review. A block of mass m1 = 2.00 kg and a block...Ch. 10 - A stepladder of negligible weight is constructed...Ch. 10 - A stepladder of negligible weight is constructed...Ch. 10 - A wad of sticky clay with mass m and velocity vi...Ch. 10 - Prob. 76PCh. 10 - Prob. 77PCh. 10 - Review. A string is wound around a uniform disk of...Ch. 10 - Prob. 79PCh. 10 - Prob. 80PCh. 10 - A projectile of mass m moves to the right with a...Ch. 10 - Figure P10.82 shows a vertical force applied...Ch. 10 - A solid sphere of mass m and radius r rolls...Ch. 10 - Prob. 84PCh. 10 - BIO When a gymnast performing on the rings...
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
- Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r, u, and t, respectively. Consider the quantity (3u2t). (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?arrow_forwardFind the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forwardThe cross product AxB is perpendicular to both vectors in the cross product (think of Aand В as lying on a sheet of paper; the cross product is perpendicular to the plane of the sheet). After figuring out the two directions perpendicular to both vectors you use one of the right hand rules given on Page 338 to choose which of the two direction is correct. All three should give the same result so use whichever one you are most comfortable with. In class, we will use the middle one in the diagram in the book. The vector torque is where "is the vector from the axis of rotation to where the force is applied. Which is the direction of the torque vector? +y ++ * (in) +z (out) O = in (O) = outarrow_forward
- Consider two vectors à = (1, – 3,0) and B = (0 ,0,7). Let C be their cross product: Č = Ã × В. a) Calculate the Cartesian components of C. b) What is the angle between vectors B and C?arrow_forwardI need help with this problem and an explanation for the solution described below. (University Physics 1: Vectors)arrow_forwardProblem 1: Let A = î - 2ĵ and B = 2î + ĵ. Compute A.B. Problem 2: Let A = î - 2ĵ and B = 2î + ĵ. Compute A. (A + B). 1 Problem 3: Using the dot product, compute the angle between vectors C and D. C = 2î + 3ĵ D = 3î - 5ĵarrow_forward
- I am stuck on how to do this problem.arrow_forwardEXPLAIN EACH LETTER Question 1.1: Calculate the dot product of vectors A and B, where |A-5 and |B|=3. A A A A B B a. b. d. с.arrow_forwardFor vectors ū and ū, suppose ||ü|| - 5, the angle between the vectors is 170 degrees, and the dot product ü-i = -8. Find the magnitude of vector i . Leave at least 4 decimals place. Don't round.arrow_forward
- 4G li. 12:23 SDD1-4E7C-44C7-A86A-F33B0962698C.j → ... 8. Find the vector product of two vectors A = 50 and B| = 20, with an angle between them is 45°.arrow_forwardQuestion 1arrow_forwardi know we have to use cross product and dot product but how do we determine the "two" possible values for these vectors? dont we just take the smallest of the two? please explain how we get two possible values of scalar product.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Rotational Kinetic Energy; Author: AK LECTURES;https://www.youtube.com/watch?v=s5P3DGdyimI;License: Standard YouTube License, CC-BY