Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 426

A spring of spring constant \(10^{3} \mathrm{~N} / \mathrm{m}\) is stretched initially \(4 \mathrm{~cm}\) from the unscratched position. How much the work required to stretched it further by another \(5 \mathrm{~cm}\) ? (A) \(6.5 \mathrm{NM}\) (B) \(2.5 \mathrm{NM}\) (C) \(3.25 \mathrm{NM}\) (D) \(6.75 \mathrm{NM}\)

Short Answer

Expert verified
The short answer for this question is: The amount of work required to stretch the spring further by another \(5 \mathrm{~cm}\) is approximately \(3.25 \mathrm{~N \cdot m}\), which corresponds to option (C).

Step by step solution

01

Identify the known values

We are given the spring constant \(k = 10^3 \mathrm{~N/m}\), the initial stretched length \(x_{1} = 4 \mathrm{~cm}\), and the length to be stretched further (\(5 \mathrm{~cm}\)). We need to find the work done (W) to stretch the spring by the given length.
02

Convert length to meters

The given lengths are in centimeters, and we need to convert them to meters for our calculations, since the spring constant is given in \(\mathrm{N/m}\). So, \(x_{1} = 4\mathrm{~cm} = 0.04\mathrm{~m}\) The length to be stretched further is \(5\mathrm{~cm} = 0.05\mathrm{~m}\)
03

Calculate the final stretched length

We need to find the final stretched length by adding the initial stretched length and the length to be stretched further. \(x_{2} = x_{1} + 0.05 \mathrm{~m} = 0.04\mathrm{~m} + 0.05\mathrm{~m} = 0.09\mathrm{~m}\)
04

Calculate the work done

Now, we can plug in the values into the formula of work done by the spring, which is given by Hooke's law: $$W = \frac{1}{2}k(x_{2}^2 - x_{1}^2)$$ Replacing the known values: $$W = \frac{1}{2}(10^3 \mathrm{~N/m})(0.09^2\mathrm{~m^2} - 0.04^2\mathrm{~m^2})$$ Calculating the work done: $$W \approx 3.25 \mathrm{~N\cdot m}$$
05

Compare the result with the given options

We calculated the work done to be approximately \(3.25 \mathrm{~N\cdot m}\). Comparing this result with the given options, we see that the closest answer is: (C) \(3.25 \mathrm{~N \cdot m}\)

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 bomb of \(12 \mathrm{~kg}\) divides in two parts whose ratio of masses is $1: 4 .\( If kinetic energy of smaller part is \)288 \mathrm{~J}$, then momentum of bigger part in \(\mathrm{kgm} / \mathrm{sec}\) will be (A) 38 (B) 72 (C) 108 (D) Data is incomplete

The mass of a car is \(1000 \mathrm{~kg}\). How much work is required to be done on it to make it move with a speed of \(36 \mathrm{~km} / \mathrm{h}\) ? (A) \(2.5 \times 10^{4} \mathrm{~J}\) (B) \(5 \times 10^{3} \mathrm{~J}\) (C) \(500 \mathrm{~J}\) (D) \(5 \times 10^{4} \mathrm{~J}\)

A cord is used to lower vertically a block of mass \(\mathrm{M}\) by a distance \(\mathrm{d}\) with constant downward acceleration \((9 / 2)\). Work done by the cord on the block is (A) \(-\mathrm{Mgd} / 2\) (B) \(\mathrm{Mgd} / 4\) (C) \(-3 \mathrm{Mgd} / 4\) (D) \(\mathrm{Mgd}\)

If the water falls from a dam into a turbine wheel \(19.6 \mathrm{~m}\) below, then the velocity of water at the turbine is \(\ldots \ldots\) \(\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\) (A) \(9.8 \mathrm{~m} / \mathrm{s}\) (B) \(19.6 \mathrm{~m} / \mathrm{s}\) (C) \(39.2 \mathrm{~m} / \mathrm{s}\) (D) \(98.0 \mathrm{~m} / \mathrm{s}\)

A ball is allowed to fall from a height \(20 \mathrm{~m}\). If there is \(30 \%\) loss of energy due to impact, then after one impact ball will go up to (A) \(18 \mathrm{~m}\) (B) \(16 \mathrm{~m}\) (C) \(12 \mathrm{~m}\) (D) \(14 \mathrm{~m}\)
See all solutions

Recommended explanations on English Textbooks

Global English

Read Explanation

Lexis and Semantics

Read Explanation

Research and Composition

Read Explanation

Summary Text

Read Explanation

Prosody

Read Explanation

Sociolinguistics

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