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

Whose resistance is twice that of the original resistor, Regard as a capaci...

Regard as a capacitor which is charged to 12 volts and then connected across a resistor. Allow t1/2 be the time it takes for the voltage to drop down to 6 volts. Presume the experi

What do you understand by rectifier, What do you understand by rectifier? I...

What do you understand by rectifier? Illustrate working of half wave and full wave rectifiers with diagrams. Show the expression for its efficiency? Define a transistor and illu

Determine the mass of the steam, A piston-cylinder device initially contain...

A piston-cylinder device initially contains 0.8 m 3 of saturated water vapour (steam) at 250 kPa. At this state, the piston is resting on a set of stops and the mass of the piston

How do you use operational amplifier as differentiator, How do you use oper...

How do you use operational amplifier as differentiator and adder/subtractor. Fig. shows differentiator or differentiation amplifier. As its name implies, circuit performs mathe

Curies law, Curie's law (P. Curie) The susceptibility, khi, of an isot...

Curie's law (P. Curie) The susceptibility, khi, of an isotropic paramagnetic substance is associated to its thermodynamic temperature T through the equation khi = C/T

Determine the evaporation rate, An industrial process involves the evaporat...

An industrial process involves the evaporation of water from a liquid film that forms on a contoured surface. Dry air is passed over the surface, and from laboratory measurements t

The size of nucleus is measured, The size of nucleus is measured in: (1...

The size of nucleus is measured in: (1)amu (2)Angstrom (3)Fermi (4)cm Ans: (3)Fermi

What is electric potential and electric potential energy, Q. What is the di...

Q. What is the dissimilarity between electric potential and electric potential energy? Ans: Suppose you desire to know the electric potential energy that a particular part

Binding Energy per nucleon, The average energy needed to release a nucleon ...

The average energy needed to release a nucleon from the nucleus is known as binding energy per nucleon.   Binding energy per nucleon diffrence  Stability of nucleus

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