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

What do you understand by absorption coefficient, What do you understand by...

What do you understand by "Absorption coefficient"? which is a better absorber of sound, glass or fibre glass?

Illustrates the evidence to support the big bang theory, Q. Illustrates the...

Q. Illustrates the evidence is there supporting the Big Bang theory? Answer:- In brief the universe is expanding. Each of the galaxies we have observed that are utmost awa

Motion WS, a rocket is launched upward from a building that is 29m above th...

a rocket is launched upward from a building that is 29m above the ground. the rocket was launched (upward) at 18m/s, what was the time to reach the ground below the building?

Interference fringes, If a polarizer is placed in front of each slit, what ...

If a polarizer is placed in front of each slit, what modification be observed in the interference fringes. A) when the two polarizing axes are perpendicular? b) when the two

SPECTRUM, HOW CAN A PURE SPECRUM BE PRODUCED IN THE LABOLATORY

HOW CAN A PURE SPECRUM BE PRODUCED IN THE LABOLATORY

Why capacitor blocks d.c. but allows a.c., Q. A capacitor blocks d.c. but a...

Q. A capacitor blocks d.c. but allows a.c. Why? Capacitive reactance   XC = 1/ω C        = 1 / 2πν C Where ν is the frequency of the a.c. supply. In a d.c. circuit

Illustrate light emitting diode in fibre optic communication, Illustrate th...

Illustrate the light emitting diode for fibre optic communication? Light-Emitting Diode (LED) for fibre optic communication: There are two types of LED. They are surface etc

Telescope, Working of terrestrial telescope

Working of terrestrial telescope

Coulomb law in vector form, What is the position vector of point c in equil...

What is the position vector of point c in equilateral triangle?

What path does an asteroid take, Q. Illustrate what path does an asteroid t...

Q. Illustrate what path does an asteroid take? Answer:- The asteroid will forever take the path minimizing its Lagrangian recognized as the least action principle in Lagra

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