Book edition 4th edition

Author(s) Ruth W. Chabay, Bruce A. Sherwood

Pages 1135 pages

ISBN 9781118875865

Answers without the blur.

Just sign up for free and you're in.

Short Answer

You hang a 10 kg mass from a copper wire, and the wire stretches by .
(a) If you suspend the same mass from two copper wires, identical to the original wire, what happens?
(b) If you suspend the same mass from a copper wire with half the cross-sectional area but the same length as the original wire, what happens?
(c) If you suspend the same mass from a copper wire with the same cross-sectional area but twice the length of the original wire, what happens?

(a) The stretch in the wire when two wires are used instead of one is 4 mm.

(b) The stretch in the wire when the cross-sectional area is halved is 16 mm.

(b) The stretch in the wire when the initial length is doubled is 16 mm.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

A 10 kg mass is hung from a copper wire, and the wire stretches by 8 mm.

Step 2: Change in length of the wire

The change in length of a wire of initial length L and cross-sectional area A when force F is applied to it can be expressed as,

$∆ L = \frac{FL}{AY}$ (I)

Here L is Young's modulus of the material of the wire.

Step 3: Determining the change in length when two wires are used instead of one

When two wires are used, the cross-sectional area doubles. From equation (I), the new change in length can be calculated as,

$\begin{array}{rcl} ∆ L & = & \frac{FL}{2 AY} \\ = & \frac{1}{2} (\frac{FL}{AY}) \\ = & \frac{1}{2} \times 8 mm \\ = & 4 mm \end{array}$

Thus, the new change in length is 4 mm.

Step 4: Determining the change in length when the cross-sectional area is halved

From equation (I), the new change in length when the cross-sectional area is halved can be calculated as,

$\begin{array}{rcl} ∆ L & = & \frac{FL}{\frac{A}{2} Y} \\ = & 2 (\frac{FL}{AY}) \\ = & 2 \times 8 mm \\ = & 16 mm \end{array}$

Thus, the new change in length is 16 mm.

Step 5: Determining the change in length when the initial length is doubled

From equation (I), the new change in length when the initial length is doubled can be calculated as,

$\begin{array}{rcl} ∆ L & = & \frac{F 2 L}{AY} \\ = & 2 (\frac{FL}{AY}) \\ = & 2 \times 8 mm \\ = & 16 mm \end{array}$

Thus, the new change in length is 16 mm.

Find Study Materials for

Create Study Materials

Select your language

Matter & Interactions

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Change in length of the wire

Step 3: Determining the change in length when two wires are used instead of one

Step 4: Determining the change in length when the cross-sectional area is halved

Step 5: Determining the change in length when the initial length is doubled

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Matter & Interactions

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Change in length of the wire

Step 3: Determining the change in length when two wires are used instead of one

Step 4: Determining the change in length when the cross-sectional area is halved

Step 5: Determining the change in length when the initial length is doubled

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics