Home › A Small Bead Can Slide on a Circular Hoop That Is in a Vertical Plane and Has a Radius

A Small Bead Can Slide on a Circular Hoop That Is in a Vertical Plane and Has a Radius

Written By Bishop Joyse1965 terça-feira, 15 de fevereiro de 2022 Add Comment Edit

Trouble 119P

A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of \(0.100 \mathrm{~m}\). The hoop rotates at a abiding rate of \(4.00 \mathrm{rev} / \mathrm{s}\) most a vertical bore (Fig. P5.119). (a) Detect the angle \(\beta\) at which the dewdrop is in vertical equilibrium. (Of course, it has a radial acceleration toward the axis.) (b) Is it possible for the bead to "ride" at the same elevation as the centre of the hoop? (c) What will happen if the hoop rotates at \(1.00 \mathrm{rev} / \mathrm{s}\)?

Equation Transcription:

$0.100\ m$

$4.00\ rev/s$

$\beta{}$

$1.00\ rev/s$

Text Transcription:

0.100 m

iv.00 rev/southward

\beta

1.00 rev/south

Step-by-Step Solution:

Solution 119P

Introduction

Nosotros volition utilise the centrifugal forcefulness and gravity to notice out the angle.

Stride 1

Suppose the mass of the bead is $m$ .

The athwart speed of the vertical hoop is $\omega{}=4\ rev/s=4(2\pi{})\ rad/s=25.13\ rad/s$

Then the centrifugal force at that on the bead volition be ${F}_{c}=m{\omega{}}^{2}r=m(25.13\ rad/s{)}^{2}(0.100\ m)=(63.65\ m/{s}^{2})m$

At present the bead volition be vertically stable if the weight of the bead is equal to the vertical component of the centrifugal force.

The weight of the dewdrop is

$w=mg=(9.8\ m/{s}^{2})m$

And the vertical component of the dewdrop is

$w={F}_{c}\cos{}\beta{}$

$\Rightarrow{}(9.8\ m/{s}^{2})m=(63.65\ m/{s}^{2})m\cos{}\theta{}$

$\Rightarrow{}\cos{}\theta{}=\frac{(9.8\ m/{s}^{2})}{(63.65\ m/{s}^{2})}=81.14°\approx{}81.1°$

Textbook: Sears and Zemansky'south University Physics with Modern Physics

Edition: thirteen

Author: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

ISBN: 9780321696861

cornellonsille.blogspot.com

Source: https://studysoup.com/tsg/170881/sears-and-zemansky-s-university-physics-with-modern-physics-13-edition-chapter-5-problem-119p

0 Response to "A Small Bead Can Slide on a Circular Hoop That Is in a Vertical Plane and Has a Radius"

Postar um comentário

Assinar: Postar comentários (Atom)