Chapter 16.2, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Write the formulas similar to Equations 4 for the center of mass (
*C* if the wire has density function *ρ*(*x*, *y*, *z*).

(b) Find the center of mass of a wire in the shape of the helix *x =* 2 sin *t*, *y =* 2 cos *t*, *z* = 3*t*, 0 ⩽ *t* ⩽ 2π*,* if the density is a constant *k*.

**(a)**

To determine

**To write:** The formulae for the center of mass of a thin wire which is in the shape of a space curve

Explanation

**Given data:**

The thin wire is in the shape of a space curve

Consider a thin wire which is in the shape of a space curve

The center of mass of the thin wire is located at the point

The formulae for the *x*-, *y*-, and *z*-coordinates of center of mass of the thin wire are written as follows.

**Formula for the x-coordinate of center of mass of the thin wire:**

Here,

*x*-coordinate of the point

Write the expression for the mass of the thin wire.

Write the expression for

**(b)**

To determine

**To find:** The center of mass of a thin wire which is in the shape of a helix.

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