Log out Go to App
Go to App

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 could be used to determine the masses of objects in an orbiting spacecraft by attaching the objects in question to a spring system with a known constant, observing the period of oscillation in the microgravity environment, and then calculating the object's mass referring back to SHM formula.

Step by step solution

01

Understanding the principle of Simple Harmonic Motion

In simple harmonic motion, an object oscillates back and forth due to restoring force that is directly proportional to the object's displacement. The formula relating the period of oscillation \(T\) with the mass \(m\) of the object and the spring constant \(k\) in a SHM system is \(T = 2\pi \sqrt{\frac{m}{k}}\).
02

Detect the period of Oscillation in Orbital Environment

In an orbiting spacecraft, gravity is essentially removed from the equation, which allows for a cleaner use of simple harmonic motion principles. A spring system with a known spring constant is brought onto the spacecraft with the object in question attached to it. The object is then displaced, and the period of oscillation is observed multiple times to ensure accuracy.
03

Calculation of the Mass

By rearranging the formula for the period of a SHM system, the mass of the object in question can be found with: \(m = \frac{kT^2}{4\pi^2}\) where, \(k\) is the spring constant known beforehand, and \(T\) is the noted period of oscillation. This will provide the mass of the object in the spacecraft.

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

How can a system have more than one resonant frequency?

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?

Two balls each of unknown mass \(m\) are mounted on opposite ends of a 1.5 -m-long rod of mass \(850 \mathrm{g} .\) The system is suspended from a wire attached to the center of the rod and set into torsional oscillations. If the wire has torsional constant \(0.63 \mathrm{N} \cdot \mathrm{m} / \mathrm{rad}\) and the period of the oscillations is \(5.6 \mathrm{s}\), what's the unknown mass \(m ?\)

A particle undergoes simple harmonic motion with amplitude \(25 \mathrm{cm}\) and maximum speed \(4.8 \mathrm{m} / \mathrm{s} .\) Find the (a) angular frequency, (b) period, and (c) maximum acceleration.

The total energy of a mass-spring system is the sum of its kinetic and potential energy: \(E=\frac{1}{2} m v^{2}+\frac{1}{2} k x^{2} .\) Assuming \(E\) remains constant, differentiate both sides of this expression with respect to time and show that Equation 13.3 results. (Hint: Remember that \(v=d x / d t .)\)
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Thermodynamics

Read Explanation

Mechanics and Materials

Read Explanation

Force

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Medical 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.

Sign-up for free