/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q17P Expand the triple product for a=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q17P (page 285)

Expand the triple product for a=蝇脳(蝇脳r) given in the discussion of Figure 3.8. If is perpendicular to w(Problem 16), show that a=鈥�蝇2r, and so find the elementary result that the acceleration is toward the center of the circle and of magnitude v2r.

Short Answer

Expert verified

The acceleration a=蝇蝇.r鈥�r蝇2

a=v2r Is proved.

Step by step solution

01

Given condition

The given condition is, a=ww.r鈥�rw2.

02

Concept Used

The value of a triple vector product is a linear combination of the two vectors in the parenthesis; the coefficient of each vector is the dot product of the other two; the middle vector in the triple product always has the positive sign.

03

Determine the Acceleration

Using the identity of the vector triple product:

A脳B脳C=BC.A鈥�CB.Aa=蝇蝇.r鈥�r蝇.蝇a=蝇蝇.r鈥�r蝇2.

The acceleration a=蝇蝇.r鈥�r蝇2

04

Determine the equation

The perpendicular vectors are given as follows,

From 蝇is perpendicular to r,蝇.r=0

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) Given 桅=x2-y2, sketch on one graph the curves桅=4,桅=1,桅=0,桅=-1,桅=-4. If桅is the electrostatic potential, the curves桅=const. are equipotential, and the electric field is given byE=-鈭�桅. If桅is temperature, the curves桅= const. are isothermals and鈭�桅is the temperature gradient; heat flows in the direction-鈭�桅.

(b) Find and draw on your sketch the vectors-鈭�桅at the points(x,y)=(+1,+1),(0,+2),(+2,0),. Then, remembering that鈭�桅is perpendicular to桅= const., sketch, without computation, several curves along which heat would flow [see (a)].

鈭�2xdy-3ydxaround the square with vertices(0,2),(2,0),(-2,0),(0,-2).

For the force field F=-yi+xj+zk, calculate the work done in moving a particle from (1,0,0) torole="math" localid="1664273455603" (-1,0,蟺)

(a) along the helixx=cost,y=sint,z=t;

(b) along the straight line joining the points.

If A and B are the diagonals of a parallelogram, find a vector formula for the area of the parallelogram.

A cylindrical capacitor consists of two long concentric metal cylinders. If there is a charge of k coulombs per meter on the inside cylinder of radius, R1and coulombs per meter on the outside cylinder of radius,R1find -k the electric field E between the cylinders. Hint: Use Gauss鈥檚 law and the method indicated in Figure 10.7. What is E inside the inner cylinder? Outside the outer cylinder? (Again use Gauss鈥檚 law.) Find, either by inspection or by direct integration, the potential role="math" localid="1659237306724" 蠁such thatE=-鈭�蠁for each of the three regions above. In each case E is not affected by adding an arbitrary constant to蠁. Adjust the additive constant to make蠁a continuous function for all space
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Famous Physicists

Read Explanation

Engineering Physics

Read Explanation

Quantum Physics

Read Explanation

Scientific Method Physics

Read Explanation

Space Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.