Bead sliding on wire, Physics

Assignment Help:

Bead Sliding on Wire

A vertical hoop supports a wire which is attached from the top of the hoop to any other point. Illustrate that the time required for a frictionless bead to slide down the wire is the same for any destination point.  A relevant kinematics equation is

x = v0t +1/2at2.           

935_Bead Sliding on Wire.png

The acceleration is g cos θ. Since v0 is zero we can write

x =1/2(cosθgt2).

But x = 2Rcos θ from geometry. So

2Rcosθ =1/2(cosθgt2)

2R =1/2(gt2)

And,

t = 2√R/g,

Which is independent of the angle θ, and depends only on the radius of the hoop and the acceleration due to gravity.

Note that the problem and its solution is unchanged if one end of the wire is connected to the bottom of the hoop instead of the top.

Sir James Jeans, in his remarkable book "An Elementary Treatise on The-oretical Mechanics" noted that the solution suggests an interesting mini-mization problem. Namely, where to place a wire from a fixed point to aninclined plane such that the time for a bead to slide from the point to the plane is a minimum?

The practical form of the solution is to configure a vertical hoop in a plane at a 90 degree angle to the ramp with its top at the fixed point P and to adjust its diameter until it just touches the

1285_Bead Sliding on Wire1.png

ramp at point T. A wire from the top to the point of tangency will provide the least time. Why? Because every other path from the point will touch the hoop at the same time, but the wire chosen is the only one which will have reached the plane in this time.


Related Discussions:- Bead sliding on wire

Schrodinger Equation, For what purpose do we use Schrodinger equation in ou...

For what purpose do we use Schrodinger equation in our daily life?

Michealson interferometer, describe the principle, construction and working...

describe the principle, construction and working of Michelson Interferometer.

Experiment of a simple tripod, A simple tripod A useful tripod can be m...

A simple tripod A useful tripod can be made by cutting away the sides of a tin can. It is suitable to make two or three of these to suit dissimilar burners and for use as stand

Mechanics, components of force in two given direction

components of force in two given direction

Physics help, The driver of an SUV slammed on the breaks when he saw a tree...

The driver of an SUV slammed on the breaks when he saw a tree 52 m away blocking the road. The SUV slowed down at a constant rate of 4.0 m/s2 for 3.6 s before reaching the tree. Wh

Quantum particle confined to one dimensional box, A quantum particle confin...

A quantum particle confined to one dimensional box of width 'a' is in its first exited state. What is the probability of finding the particle over an interval of (a/2) marked symme

Write any four characteristics of electromagnetic waves, Write any four cha...

Write any four characteristics of electromagnetic waves. Give two uses each of 1. Radio-waves 2. Micro-waves.

Show the conditions for total internal reflection, Show the conditions for ...

Show the conditions for total internal reflection to happen. Arrive at the relation between refractive index and critical angle. What do you mean by optical fibre? on what rules do

Blackbody radiation, blackbody radiation The radiation the radiance at...

blackbody radiation The radiation the radiance at specific frequencies all across the spectrum generated by a blackbody i.e., a perfect radiator (and absorber) of heat. Physic

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd