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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

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Most popular questions from this chapter

Problem26,but integrate over the open surface obtained by leaving out the face of the cube in the(x,y) plane.

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Find vector fields A such that V=curlAfor each given V.

V=-K

鈭�C鈥�(x2鈭�y)dx+(x+y3)dy: where Cis the parallelogram with vertices (0,0),(2,0),(1,1),(3,1).

Find, 鈭�r, wherer=x2+y2 , using (6.7) and also using (6.3). Show that your results are the same by using (4.11) and (4.12).
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