Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 976

Cross-sectional area o if wire of length \(L\) is \(A\). Young's modulus of material is \(\mathrm{Y}\). If this wire acts as a spring what is the value of force constant? (A) (YA/L) (B) (YA/2L) (C) (2YA/L) (D) ( \(\mathrm{YL} / \mathrm{A})\)

Short Answer

Expert verified
The correct value of the force constant is (A) (YA/L).

Step by step solution

01

Recall Hooke's Law

Hooke's Law states that the force acting on a spring is proportional to the displacement of the spring from its equilibrium position. Mathematically, it is given by: \(F = -kx\) Where F is the force, k is the spring constant (or force constant), and x is the displacement of the spring from its equilibrium position.
02

Relate stress and strain using Young's modulus

We have to relate the force F to the length L and cross-sectional area A of the wire. To do this, we use the definition of Young's modulus, which states the relationship between stress and strain: \(Y = \dfrac{\text{stress}}{\text{strain}}\) Stress is defined as the force per unit area, while strain is defined as the change in length per unit length. We can write these definitions mathematically as: \(\text{stress} = \dfrac{F}{A}\) and \(\text{strain} = \dfrac{\Delta L}{L}\)
03

Find the force constant using Hooke's Law and Young's modulus

Now, we can substitute the expressions for stress and strain in the Young's modulus equation: \(Y = \dfrac{\dfrac{F}{A}}{\dfrac{\Delta L}{L}}\) Next, we solve this equation for the force F: \(F = \dfrac{YA}{L}\Delta L\) By comparing this equation with Hooke's Law, we can see that the force constant, k, is given by: \(k = \dfrac{YA}{L}\)
04

Find the value of the force constant in the given options

Now, we can find the force constant value in the given options: (A) (YA/L) (B) (YA/2L) (C) (2YA/L) (D) (YL/A) We derived the force constant, k, as (YA/L), which matches option (A). Therefore, the correct answer is: (A) (YA/L)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A thin liquid film formed between a u-shaped wire and a light slider supports a weight of \(1.5 \times 10^{-2} \mathrm{~N}\) (see figure). The length of the slider is \(30 \mathrm{~cm}\) and its weight negligible. The surface tension of the liquid film is. (A) \(0.0125 \mathrm{Nm}^{-1}\) (B) \(0.1 \mathrm{Nm}^{-1}\) (C) \(0.05 \mathrm{Nm}^{-1}\) (D) \(0.025 \mathrm{Nm}^{-1}\)

The ratio of two specific heats of gas $\mathrm{C}_{\mathrm{P}} / \mathrm{C}_{\mathrm{V}}\( for Argon is \)1.6\( and for hydrogen is \)1.4 .$ Adiabatic elasticity of Argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to \(\mathrm{E}\) at the pressure. (A) \(\mathrm{P}\) (B) \((7 / 8) \mathrm{P}\) (C) \((8 / 7) \mathrm{P}\) (D) \(1.4 \mathrm{P}\)

Oxygen boils at \(183^{\circ} \mathrm{C}\). This temperature is approximately. (A) \(215^{\circ} \mathrm{F}\) (B) \(-297^{\circ} \mathrm{F}\) (C) \(329^{\circ} \mathrm{F}\) (D) \(361^{\circ} \mathrm{F}\)

Read the assertion and reason carefully and mark the correct option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. Assertion: The concept of surface tension is held only for liquids. Reason: Surface tension does not hold for gases. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

At what temperature the centigrade (celsius) and Fahrenheit readings at the same. \((\mathrm{A})-40^{\circ}\) (B) \(+40^{\circ} \mathrm{C}\) (C) \(36.6^{\circ}\) (D) \(-37^{\circ} \mathrm{C}\)
See all solutions

Recommended explanations on English Textbooks

Key Concepts in Language and Linguistics

Read Explanation

Research and Composition

Read Explanation

Single Paragraph Essay

Read Explanation

Global English

Read Explanation

Cues and Conventions

Read Explanation

Semiotics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free