Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 38

An ideal spring has the spring constant \(k=440 \mathrm{~N} / \mathrm{m}\) Calculate the distance this spring must be stretched from its equilibrium position for 25 J of work to be done.

Short Answer

Expert verified
Answer: The spring must be stretched approximately 0.336 meters from its equilibrium position.

Step by step solution

01

Recall Hooke's Law

Hooke's law states that the force exerted by a spring is equal to the spring constant multiplied by the displacement from the equilibrium position: \(F = kx\) Where \(F\) is the force exerted by the spring, \(k\) is the spring constant, and \(x\) is the displacement from the equilibrium position. In this exercise, the spring constant \(k = 440 \mathrm{~N} / \mathrm{m}\).
02

Write the expression for the work done on the spring

The work done on the spring is given by the following equation: \(W = \frac{1}{2}kx^2\) Where \(W\) is the work done, \(k\) is the spring constant, and \(x\) is the displacement from the equilibrium position. In this problem, we are given that the work done, \(W\), is 25 J.
03

Substitute the known values and solve for the displacement x

We now have: \(25 \mathrm{J} = \frac{1}{2}(440 \mathrm{~N} / \mathrm{m})(x^2)\) First, we need to isolate \(x^2\) by dividing both sides of the equation by \(\frac{1}{2}k\): \(x^2 = \frac{50 \mathrm{J}}{440 \mathrm{~N} / \mathrm{m}}\) Next, we will calculate the fraction: \(x^2 = \frac{50}{440} \mathrm{m}\) Now, we can find the square root of both sides of the equation to solve for \(x\): \(x = \sqrt{\frac{50}{440}} \mathrm{m}\) Finally, let's approximate the distance: \(x \approx 0.336 \mathrm{m}\)
04

State the final answer

Therefore, the spring must be stretched approximately 0.336 meters from its equilibrium position for 25 J of work to be done.

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 force of \(5.00 \mathrm{~N}\) acts through a distance of \(12.0 \mathrm{~m}\) in the direction of the force. Find the work done.

A driver notices that her 1000 , \(\mathrm{kg}\) car slows from \(v_{0}=\) \(90.0 \mathrm{~km} / \mathrm{h}(25.0 \mathrm{~m} / \mathrm{s})\) to \(v=70.0 \mathrm{~km} / \mathrm{h}(19.4 \mathrm{~m} / \mathrm{s})\) in \(t=6.00 \mathrm{~s}\) moving on level ground in neutral gear. Calculate the power needed to keep the car moving at a constant speed, \(v_{\text {ave }}=\) \(80.0 \mathrm{~km} / \mathrm{h}(22.2 \mathrm{~m} / \mathrm{s})\)

A car does the work \(W_{\text {car }}=7.0 \cdot 10^{4} \mathrm{~J}\) in traveling a distance \(x=2.8 \mathrm{~km}\) at constant speed. Calculate the average force \(F\) (from all sources) acting on the car in this process.

A softball, of mass \(m=0.250 \mathrm{~kg}\), is pitched at a speed \(v_{0}=26.4 \mathrm{~m} / \mathrm{s}\). Due to air resistance, by the time it reaches home plate it has slowed by \(10.0 \% .\) The distance between the plate and the pitcher is \(d=15.0 \mathrm{~m}\). Calculate the average force of air resistance, \(F_{\text {air }}\) that is exerted on the ball during its movement from the pitcher to the plate.

A car of mass \(m=1250 \mathrm{~kg}\) is traveling at a speed of \(v_{0}=105 \mathrm{~km} / \mathrm{h}(29.2 \mathrm{~m} / \mathrm{s}) .\) Calculate the work that must be done by the brakes to completely stop the car.
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Modern Physics

Read Explanation

Space Physics

Read Explanation

Medical Physics

Read Explanation

Electrostatics

Read Explanation

Measurements

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