Chapter 5: Q28P (page 257)

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The mass of a wire bent in the shape of the arc if its density (mass per unit length) is.

Short Answer

Expert verified

The mass of a wire bent in the shape of the arc is $\frac{13}{6}$ .

Step by step solution

Definition of Mass

A physical body's mass is the amount of matter it contains. It is also a measure of the body's inertia, or resistance to acceleration (velocity change) when a net force is applied.

Determination of the Mass of the wire

Calculate the mass of the wire.

$M = \int λ d s = \int_{0}^{2} \sqrt{x} \sqrt{1 + y^{c 2}} d x = \int_{0}^{2} \sqrt{x} \sqrt{1 + \frac{1}{4 x}} d x = \int_{0}^{2} \sqrt{x + \frac{1}{4} d (x + \frac{1}{4})} = \frac{2}{3} {(x + \frac{1}{4})}^{3 / 2} = \frac{2}{3} [\frac{27}{8} - \frac{1}{8}] = \frac{13}{6}$

Thus, the mass of the bent wire is

\frac{13}{6}

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In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The mass of a wire bent in the shape of the arc if its density (mass per unit length) is.

Short Answer

Step by step solution

Definition of Mass

Determination of the Mass of the wire

One App. One Place for Learning.

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In Problems 17 to 30, for the curve y=x, betweenx=0 andx=2 , find:The mass of a wire bent in the shape of the arc if its density (mass per unit length) is.

Short Answer

Step by step solution

Definition of Mass

Determination of the Mass of the wire

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Astrophysics

Fields in Physics

Electric Charge Field and Potential

Quantum Physics

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Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ , find:
The mass of a wire bent in the shape of the arc if its density (mass per unit length) is.