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

Strength of material, a 10 m radius of thin spherical tank is to be used to...

a 10 m radius of thin spherical tank is to be used to store gas if the wall thickness of the tank is 10 mm and the 125 mpa the maximum possible gas pressure neglecting the radial s

Rydberg formula, Rydberg formula (Rydberg): A formula which define all...

Rydberg formula (Rydberg): A formula which define all of the characteristics of hydrogen's spectrum, comprising the Lyman, Paschen, Balmer, Pfund series and Brackett,. For

Subtracting 2 vectors, Subtracting 2 Vectors This is where things obtai...

Subtracting 2 Vectors This is where things obtain a bit more interesting. What we required to note here is in which in Physics a negative sign simply means "in the opposite dir

Determine the wavelength of the traveling wave, A string has a linear densi...

A string has a linear density of 7.20 10-3 kg/m and is under a tension of 390 N. The string is 1.9 m long, is fixed at both ends, and is vibrating in the standing wave pattern sho

Scientific activity, the factors which decide the broad area of scientific ...

the factors which decide the broad area of scientific activity ?

Describe the numerical aperture in the optical fibre, Describe the numerica...

Describe the numerical aperture in the optical fibre. Numerical Aperture: The numerical aperture is described as the sine of the acceptance angle. Therefore, Numerical

Mechanics, components of force in two given direction

components of force in two given direction

Is soccer balls go faster in the air on a cold or hot day, Q. Illustrate th...

Q. Illustrate that soccer balls go faster in the air on a cold or hot day? Answer:- On a hot day the air molecules have additional kinetic energy they move around more fre

Rayleigh-jeans law, Rayleigh-Jeans law For any blackbody at thermodyna...

Rayleigh-Jeans law For any blackbody at thermodynamic temperature T, the radiancy R onto a range of frequencies among nu & nu + dnu is provided by R = 2 pi nu 2 k T/c 2 .

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