Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 46

A pendulum of length \(L\) is mounted in a rocket. Find its period if the rocket is (a) at rest on its launch pad; (b) accelerating upward with acceleration \(a=\frac{1}{2} g ;\) (c) accelerating downward with \(a=\frac{1}{2} g ;\) and \((d)\) in free fall.

Short Answer

Expert verified
The pendulum's period when the rocket is: (a) at rest will be \(T=2\pi\sqrt{\frac{L}{g}}\), (b) accelerating upward will be \(T=2\pi\sqrt{\frac{L}{\frac{3}{2}g}}\), (c) accelerating downward will be \(T=2\pi\sqrt{\frac{L}{\frac{1}{2}g}}\) and (d) in free fall will be undefined as there will be no swing.

Step by step solution

01

Obtain the pendulum's period

For a simple pendulum, the period \(T\) is given by the formula \(T=2\pi\sqrt{\frac{L}{g}}\), where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity.
02

Calculate the period at rest

When the rocket is at rest, \(g\) stays the usual gravitational acceleration. Hence, the period will be \(T=2\pi\sqrt{\frac{L}{g}}\).
03

Calculate the period during upward acceleration

When the rocket is accelerating upwards, the pendulum experiences an increase in the effective gravitational force. This will be equal to \(g+a=g+\frac{1}{2}g=\frac{3}{2}g\). Hence, the period will be \(T=2\pi\sqrt{\frac{L}{\frac{3}{2}g}}\).
04

Calculate the period during downward acceleration

When the rocket is accelerating downwards, the pendulum experiences a reduction in the effective gravitational force. This will be equal to \(g-a=g-\frac{1}{2}g=\frac{1}{2}g\). Hence, the period will be \(T=2\pi\sqrt{\frac{L}{\frac{1}{2}g}}\).
05

Calculate the period during free fall

During free fall, the rocket experiences no net gravitational force as it is in a state of weightlessness. Therefore, the pendulum won't swing and its period will be undefined.

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

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

When in its cycle is the acceleration of an undamped simple harmonic oscillator zero? When is the velocity zero?

A wheel rotates at 600 rpm. Viewed from the edge, a point on the wheel appears to undergo simple harmonic motion. What are (a) the frequency in \(\mathrm{Hz}\) and (b) the angular frequency for this SHM?

The protein dynein powers the flagella that propel some unicellular organisms. Biophysicists have found that dynein is intrinsically oscillatory, and that it exerts peak forces of about \(1.0 \mathrm{pN}\) when it attaches to structures called microtubules. The resulting oscillations have amplitude \(15 \mathrm{nm}\). (a) If this system is modeled as a mass-spring system, what's the associated spring constant? (b) If the oscillation frequency is \(70 \mathrm{Hz}\), what's the effective mass?

Show that \(x(t)=a \cos \omega t-b \sin \omega t\) represents simple harmonic motion, as in Equation \(13.8,\) with \(A=\sqrt{a^{2}+b^{2}}\) and \(\phi=\tan ^{-1}(b / a)\)
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Kinematics Physics

Read Explanation

Dynamics

Read Explanation

Quantum Physics

Read Explanation

Radiation

Read Explanation

Mechanics and Materials

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