Q. 53 Use Exercise 52 to show that dNd... [FREE SOLUTION]

Chapter 11: Q. 53 (page 890)

Use Exercise 52 to show that $\frac{d N}{d s} = - k T + 味 B,$ where 魏 is the curvature. (Hint: Differentiate N = B 脳 T with respect to arc length.)

Short Answer

Expert verified

The given statement is proved.

Step by step solution

Step 1. Given Information.

The Relationship between $\frac{d T}{d s}, 魏, and N$ can be defined as letting C be the graph of a vector function r(s) defined on an intervalI and parametrized by

arc length s. If the unit tangent vector T has a nonzero derivative, then $\frac{d T}{d s} = 魏 N .$

Step 2. Showing that dNds=-kT+ζB.

To show that $\frac{d N}{d s} = - k T + 味 B,$ where 魏 is the curvature, we will use the relationship between $\frac{d T}{d s}, 魏, and N .$

By using the relationship,

role="math" localid="1649676899612" $\frac{d T}{d s} = \frac{d}{d s} (N) = \frac{d}{d s} (B 脳 T) [N = B 脳 T] = \frac{d B}{d s} 脳 T + B 脳 \frac{d T}{d s} = 鈭� 味 N 脳 T + B 脳 k N [\frac{d B}{d s} = 鈭� 味 N and \frac{d T}{d s} = k N] = 味 B - k T [B 脳 N = - T a n d - N 脳 T = B]$

Hence proved.

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91影视

Use Exercise 52 to show that $\frac{d N}{d s} = - k T + 味 B,$ where 魏 is the curvature. (Hint: Differentiate N = B 脳 T with respect to arc length.)

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Showing that dNds=-kT+ζB.

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91影视

Use Exercise 52 to show that dNds=-kT+味B, where 魏 is the curvature. (Hint: Differentiate N = B 脳 T with respect to arc length.)

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Showing that dNds=-kT+ζB.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use Exercise 52 to show that $\frac{d N}{d s} = - k T + 味 B,$ where 魏 is the curvature. (Hint: Differentiate N = B 脳 T with respect to arc length.)