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

Explain about the monochromaticity of laser, Explain about the monochromati...

Explain about the monochromaticity of laser. Monochromaticity: The light emitted through a laser is monochromatic, that is this is of one wavelength (colour). Although in ca

What is sarah horizontal acceleration, Alfonso and Sarah like to go sky div...

Alfonso and Sarah like to go sky diving together. Alfonso has a mass of 88 kg, and Sarah has a mass of 66 kg. While in free fall together, Alfonso pushes Sarah horizontally with a

PHYSICS, WHAT IS THE MEAN OF HEAT

WHAT IS THE MEAN OF HEAT

Damped simple harmonic motion, Damped Simple Harmonic Motion Adding a d...

Damped Simple Harmonic Motion Adding a damping force proportional to x to the equation of easy harmonic motion, the first derivative of x along with respect to time, the equati

Determine the forward current for a forward voltage, The graph shown in Fig...

The graph shown in Figure was obtained during an experiment on a diode. (a) What type of diode is this? Give reasons. (b) Determine the forward current for a forward voltage

Rayleigh criterion, Rayleigh criterion; resolving power: A criterion f...

Rayleigh criterion; resolving power: A criterion for finding out how finely a set of optics might be able to distinguish. It start with the supposition that central ring of on

Quantum theory of light, Quantum Theory of Light: Wave theory failed to...

Quantum Theory of Light: Wave theory failed to describe some new effects in 19th century. A German Physicist Max Plank gave theory about the nature of light. 1. Light is emi

Determine watts of power dissipated for potential difference, The constant ...

The constant potential difference across a 2 ohm resistor is 20 volts. How many watts of power are dissipated by this resistor? Ans: 200 watts of power are dissipated throug

Michelson interferometer, Ask question 15. When the movable mirror of a Mic...

Ask question 15. When the movable mirror of a Michelson''s interferometer is moved through a distance of 0.03mm, 100 fringes are displaced, what is the wavelength and color of the

PHYSICS PRACTICAL., I WANT SHORT THEORY OF DEFLECTION MANGNETOMETER TAN A& ...

I WANT SHORT THEORY OF DEFLECTION MANGNETOMETER TAN A& TAN B

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