(a) Explanation Given data: The thin wire is in the shape of a space curve C and the density function of the wire is ρ ( x , y , z ) . Consider a thin wire which is in the shape of a space curve C and the density function of the wire is ρ ( x , y , z ) at the point ( x , y , z ) . The center of mass of the thin wire is located at the point ( x ¯ , y ¯ , z ¯ ) . 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: x ¯ = 1 m ∫ C x ρ ( x , y , z ) d s (1) Here, m is the mass of the thin wire, x is the x -coordinate of the point ( x , y , z ) , ρ ( x , y , z ) is the density function of the wire, and d s is the change in surface. Write the expression for the mass of the thin wire. m = ∫ C ρ ( x , y , z ) d s (2) Write the expression for d s (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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Question

Chapter 16.2, Problem 37E

(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 C .

(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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Chapter 16.2, Problem 36E

Chapter 16.2, Problem 38E

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Chapter 16 Solutions

Calculus, Early Transcendentals

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The formulae for the center of mass of a thin wire which is in the shape of a space curve C .

Solution Summary: The formula for the center of mass of a thin wire is underset_(stackrel

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

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

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Chapter 16 Solutions