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

Weber, Weber; Wb (after W. Weber, 1804-1891): The derived SI unit of m...

Weber; Wb (after W. Weber, 1804-1891): The derived SI unit of magnetic flux equivalent to the flux that, relating a circuit of one turn, generates in it an electromotive force

Holography.., What is holographic microscopy

What is holographic microscopy

What is described by millikan experiment?, The Millikan experiment showed t...

The Millikan experiment showed that electric charge was: a) Negative b) Quantized c) Positive d) Immeasurable Ans: The Millikan experiment showed that elec

Optometry, I need to know the Physics of Laser operations on eyes. Please s...

I need to know the Physics of Laser operations on eyes. Please send examples as well.

Proton was discovered, Proton was discovered by: (1)Chadwick (2)Thom...

Proton was discovered by: (1)Chadwick (2)Thomson (3)Goldstein (4)Bohr Ans: (3)Goldstein

Electric field to be non-zero at a point in space, Is it probable for the e...

Is it probable for the electric field to be non-zero at a point in space where the electric potential is zero? Ans: Regard as for instance the case of an electric potential

Introduce concept about the carbon dioxide laser, Introduce concept about t...

Introduce concept about the carbon dioxide laser. A test target is vaporized and bursts within flame onto irradiation through a high power continuous wave carbon dioxide laser

What is pair production and pair annihilation, Q. What is pair production a...

Q. What is pair production and pair annihilation? Pair production: The conversion of a photon in to an electron-positron pair on its interaction with the strong electric fie

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