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

Estimate the frequency of sound, Suppose you blow the top of a bottle and h...

Suppose you blow the top of a bottle and hear a resonance sound (standing wave).  The length of the bottle is about 25cm.  If the speed of sound in air is about 340 cm/sec., what i

Rutherford’s gold - foil experiment , An α particle is a positively charged...

An α particle is a positively charged particle. Rutherford observed the behaviour of these particles when they approach the interior of the atoms as shown in fig.  Rutherford ob

What is alpha decay and beta decay, The graph below shows a sequence of alp...

The graph below shows a sequence of alpha and beta decays, labeled 1, 2, 3, and 4. Consult Table 30-1 as required.   a) Which shows alpha decays, and which represen

Infra-red detectors, Part A) Infra-Red (IR) Detectors: An IR detector...

Part A) Infra-Red (IR) Detectors: An IR detector has an impedance of Z= (400+j200) ? . . During design tests the detector current is measured as 4 µA. What is

Ray optics., a glass prism in the shape of a quaeter-cylinder lies on the t...

a glass prism in the shape of a quaeter-cylinder lies on the table.a uniform,horizontal light falls on its vertical plane surface,as shown in the figure.if the radius of the cylind

Evaluate the height to which the center of the baton travels, A baton twirl...

A baton twirler throws a spinning baton directly upward. As it goes up and returns to the twirler's hand, the baton turns through four revolutions. Ignoring air resistance and assu

Angular velocity, Three children are riding on the edge of a merry-go-round...

Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If

What are ferrites, What are ferrites? Ferrites are ceramic compounds ha...

What are ferrites? Ferrites are ceramic compounds having trivalent metal having three valence electrons, iron and oxide of divalent element

Logic gates, working project related to logic gates

working project related to logic gates

Dimension of unit impulse, Dimension of unit impulse DIMENSION ? The di...

Dimension of unit impulse DIMENSION ? The dimension of impulse is [MLT -1 ]

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