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

State the applications of JFET, State the Applications of JFET FET is u...

State the Applications of JFET FET is used as a (1)  Buffer amplifier (2)  Low Noise Amplifier (3)  Cascaded Amplifier (4)  Analog Switch (5)  Chopper (6)  Ph

The wheatstone bridge, The wheatstone bridge: You have already solved r...

The wheatstone bridge: You have already solved resistor networks using Ohm's law and Kirchoff's laws.  In this unit we are going to look at a special arrangement of series and

Ferrits, Detail information about ferrits also current research on ferrits

Detail information about ferrits also current research on ferrits

How can lenz law explain law of conservation of energy??, Lenz''s Law state...

Lenz''s Law states that the Nature of induced emf in the coil is such that it opposes the causes of it. It can be explained by a simple understanding of Faraday EM induction ex

Newtons law of inertia truck and ladder, Newtons law of inertia Truck and L...

Newtons law of inertia Truck and Ladder As per to Newton's first law, an object in motion continues within motion along with the similar speed and in the similar direction unle

Work and energy, a person holds of hay over his head for 30 min and gets ti...

a person holds of hay over his head for 30 min and gets tired . has he done some wirk or not? justify your answer

Stefan-boltzmann law, Stefan-Boltzmann law (Stefan, L. Boltzmann): The...

Stefan-Boltzmann law (Stefan, L. Boltzmann): The radiated power P (it is rate of emission of electromagnetic energy) of hot body is proportional to the radiating surface area,

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