/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 A \(50.0-\mathrm{g}\) object is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 20

A \(50.0-\mathrm{g}\) object is attached to a horizontal spring with a force constant of \(10.0 \mathrm{~N} / \mathrm{m}\) and released from rest with an amplitude of \(25.0 \mathrm{~cm}\). What is the velocity of the object when it is halfway to the equilibrium position if the surface is frictionless?

Short Answer

Expert verified
The velocity of the object when it is halfway to the equilibrium position is \(1.03 \, m/s\).

Step by step solution

01

Defining given values and the equation for simple harmonic motion

The given values are:- the mass \(m = 50.0 \, g = 0.05 \, kg\) (converted to kg as SI unit for mass is kg),- the spring constant \(k = 10.0 \, N/m\), - and the amplitude \(A = 25.0 \, cm = 0.25 \, m\).The object is released from rest at the amplitude A, meaning initial velocity \(v_0 = 0 \, m/s\), and it's asked for the velocity when the object is halfway to the equilibrium, i.e., at \(x = A/2 = 0.125 \, m\).The equation for simple harmonic motion is: \[v = \sqrt{\frac{k}{m}} \sqrt{A^2 鈭� x^2}\]where \(v\) is the instantaneous velocity of the object; \(k\) the spring constant; \(m\) the mass; \(A\) the amplitude (maximum displacement) and \(x\) the displacement.
02

Substitution of values into the equation

Substitute the given values into the equation:\[v = \sqrt{\frac{10.0 \, N/m}{0.05 \, kg}} \sqrt{(0.25 \, m)^2 鈭� (0.125 \, m)^2}\]
03

Calculation

Now, compute the value to gain the velocity:\[v = \sqrt{200 \, s^鈥�2} \sqrt{0.25^2 \, m^2 鈭� 0.125^2 \, m^2} = 14.14 \, m/s \sqrt{0.046875 \, m^2} = 1.03 \, m/s\]

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 horizontal spring attached to a wall has a force constant of \(k=850 \mathrm{~N} / \mathrm{m}\). A block of mass \(m=1.00 \mathrm{~kg}\) is attached to the spring and rests on a frictionless, horizontal surface as in Figure P13.21. (a) The block is pulled to a position \(x_{i}=6.00 \mathrm{~cm}\) from equilibrium and released. Find the potential energy stored in the spring when the block is \(6.00 \mathrm{~cm}\) from equilibrium. (b) Find the speed of the block as it passes through the equilibrium position. (c) What is the speed of the block when it is at a position \(x_{i} / 2=3.00 \mathrm{~cm}\) ?

The distance between two successive minima of a transverse wave is \(2.76 \mathrm{~m}\). Five crests of the wave pass a given point along the direction of travel every \(14.0 \mathrm{~s}\). Find (a) the frequency of the wave and (b) the wave speed.

Ocean waves are traveling to the east at \(4.0 \mathrm{~m} / \mathrm{s}\) with a distance of \(20 \mathrm{~m}\) between crests. With what frequency do the waves hit the front of a boat (a) when the boat is at anchor and (b) when the boat is moving westward at \(1.0 \mathrm{~m} / \mathrm{s}\) ?

Transverse waves with a speed of \(50.0 \mathrm{~m} / \mathrm{s}\) are to be produced on a stretched string. A \(5.00-\mathrm{m}\) length of string with a total mass of \(0.0600 \mathrm{~kg}\) is used. (a) What is the required tension in the string? (b) Calculate the wave speed in the string if the tension is \(8.00 \mathrm{~N}\).

A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of \(8.50 \mathrm{~cm}\). If the cork is \(10.0 \mathrm{~m}\) from shore, how long does it take a ripple passing the cork to reach the shore?
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Physics of Motion

Read Explanation

Linear Momentum

Read Explanation

Electricity

Read Explanation

Magnetism

Read Explanation

Fields in Physics

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.