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

Kinematics, A particle moving in a straight line with constant accelaration...

A particle moving in a straight line with constant accelaration is having initial velocity of 10 m/s. After some time, the velocity becomes 30 m/s. Find the velocity of particle at

Illustrate double-beam oscilloscope, For the double-beam oscilloscope displ...

For the double-beam oscilloscope displays shown in Figure, determine (a) their frequency (b) their r.m.s. values (c) their phase difference. The 'time/cm' switch is on 10

When is it best to switch on the auxiliary engine, A rocket is intended to ...

A rocket is intended to leave the Earth's gravitational ?eld. The fuel in its key engine is a little less than the amount that is essential, and an auxiliary engine, only capa

Determine the mass of the steam, A piston-cylinder device initially contain...

A piston-cylinder device initially contains 0.8 m 3 of saturated water vapour (steam) at 250 kPa. At this state, the piston is resting on a set of stops and the mass of the piston

Working of compound microscope, Working of Compound Microscope: The obj...

Working of Compound Microscope: The object under examination is placed in front of the objective. The objective forms it's real and inverted image with in the focal length of t

Draw a free-body diagram for the space shuttle, Draw a free-body diagram fo...

Draw a free-body diagram for the space shuttle just after it leaves the ground.  Recognize the forces acting on the shuttle. Make sure that you do not neglect air resistance.

What is the condition for resonance, What is the condition for resonance? ...

What is the condition for resonance? Condition for resonance: The condition of frequency of the oscillatory circuit is equal to frequency of the vibrating rod as: 1/(2 Π

Hoop conjecture, Hoop conjecture (K.S. Thorne, 1972): The conjecture (...

Hoop conjecture (K.S. Thorne, 1972): The conjecture (as still unproven, though there is substantial evidence to hold up it) that a nonspherically compressed, nonspherical obje

Determine the actual distance from first face, A small air bubble is inside...

A small air bubble is inside a cube of 0.21 m. When viewed from one face it seems to be at a depth of 0.06 m, when viewed from opposite face the bubble seems to be at a depth of 0.

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