/*! 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 8 Explain how simple harmonic moti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 8

Explain how simple harmonic motion might be used to determine the masses of objects in an orbiting spacecraft.

Short Answer

Expert verified
The principle of Simple Harmonic Motion can be applied in an orbiting spacecraft to determine the masses of objects by setting up the objects to oscillate. The measured time period of these oscillations can then be related to the mass of the objects using the formula for SHM. This is possible because in the microgravity environment of an orbiting spacecraft, disturbed objects oscillate in SHM.

Step by step solution

01

Understanding Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. In simple terms, SHM occurs when the acceleration and displacement of an object are proportional and the acceleration is opposite the direction of displacement.
02

Applying Simple Harmonic Motion in Space

When an object is in orbit, it experiences a type of free-fall which creates a microgravity environment. In such a scenario, if we make a small disturbance to an object, it will start oscillating in a simple harmonic motion. The period of this oscillating motion is independent of the amplitude of the oscillation, but depends on properties such as the mass of the object and the 'springiness' of the system.
03

Determining Mass of the Objects

The mass \( m \) of an object can be determined using the concept of SHM. If \( T \) is the time period of oscillation, the spring constant \( k \), also known as the stiffness of the system and \( m \) is the mass of the object, then according to the relation in SHM, the time period \( T = 2\pi \sqrt{\frac{m}{k}} \). If we measure the time period \( T \) of the object's oscillations and we know the spring constant \( k \), we can rearrange this equation and use it to find the mass \( m = \frac{T^2 k} {4 \pi^2} \).

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

What will happen to the period of a mass-spring system if it's placed in a jetliner accelerating down a runway? What will happen to the period of a pendulum in the same situation?

The vibration frequency of a hydrogen chloride molecule is \(8.66 \times 10^{13} \mathrm{Hz}\). How long does it take the molecule to complete one oscillation?

The \(x\) - and \(y\) -components of an object's motion are harmonic with frequency ratio \(1.75: 1 .\) How many oscillations must each component undergo before the object returns to its initial position?

The muscles that drive insect wings minimize the energy needed for flight by "choosing" to move at the natural oscillation frequency of the wings. Biologists study this phenomenon by clipping an insect's wings to reduce their mass. If the wing system is modeled as a simple harmonic oscillator, by what percent will the frequency change if the wing mass is decreased by \(25 \% ?\) Will it increase or decrease?

A \(342-\mathrm{g}\) mass is attached to a spring and undergoes simple harmonic motion. Its maximum acceleration is \(18.6 \mathrm{m} / \mathrm{s}^{2}\) and its maximum speed is \(1.75 \mathrm{m} / \mathrm{s}\). Determine (a) the angular frequency, (b) the amplitude, and (c) the spring constant.
See all solutions

Recommended explanations on Physics Textbooks

Electromagnetism

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Fluids

Read Explanation

Force

Read Explanation

Engineering 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.