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

Vector Quantities: Importance and Application, What is the importance of ve...

What is the importance of vector quantities in real life? Cite some applications.

Experiment of a small spool and a large spool, A small spool and a large sp...

A small spool and a large spool Using nails for axles fasten a large spool and a smaller spool to a block of wood. Slip a rubber band in excess of both spools. Turn the larger

Equation for the equivalent capacitance, Derive mathematical equation for t...

Derive mathematical equation for the equivalent capacitance (Capacity) when capacitors are connected in series.

Ferromgntic substances, #question.An experminet to prove that a substance i...

#question.An experminet to prove that a substance is ferrmoanetic

Explain the energy and mass, Explain the Energy and Mass Albert Einstei...

Explain the Energy and Mass Albert Einstein described an intricate relationship between matter and energy.  It is summarized in the famous formula: E = mc 2   In this equ

Explain drift velocity of free electrons, Explain 'drift velocity of free e...

Explain 'drift velocity of free electrons'? Derive Ohm's law on the basis of the theory of electron drift.

Electromagnetic induction, key headings in project file of electromagnetic ...

key headings in project file of electromagnetic induction

Application for Subject Matter Expert in Physics., Hello! I would like to a...

Hello! I would like to ask if there is a job in Physics which is 24/7 Question Answering/problem solving and if any, I would like to apply for it. Thank You Prerak Dhawan

Define Displacement: , Displacement: - The modification in position of a bo...

Displacement: - The modification in position of a body in a certain direction is known as displacement. It is a vector function and its unit in SI system is meter.

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