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

Can you differentiate between half and full wave plate, Can you differentia...

Can you differentiate between half wave plate and full wave plate?

Heat, a lead bullet moves horizontally with a velocity of 130ms and embedde...

a lead bullet moves horizontally with a velocity of 130ms and embedded into a cement wall after collision. if the specific heat capacity of lead = 130J/KgC and all heat produces is

Flux, as flux = E.A and flux density is equal to flux/A then why A/A cannot...

as flux = E.A and flux density is equal to flux/A then why A/A cannot e cancelled ?

Polarisation, production and analysis of diffrent polarised light

production and analysis of diffrent polarised light

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

P2 work, what is the tension in the string when the block is lifted at a st...

what is the tension in the string when the block is lifted at a steady speed when the weight weighs 4.5N and the distance is 90cm

What are the advantages of fibre optic communication, What are the advantag...

What are the advantages of fibre optic communication? Advantages of fibre optic communication are as follows: a. Enormous band width Coaxial cable transmission of 500 M

Write the relation for the force acting on a charge, Write the relation for...

Write the relation for the force acting on a charge carrier q moving with a velocity by a magnetic field in vector notation. Using this relation, reduce the conditions under which

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