Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
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.
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
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.
Write down the electromagnetic wave equation in free space, in terms of vector and scalar potential.
how to write a paper when it is based on matlab program
A weakly guiding optical fibre propagates just two bound modes with scalar transverse electric fields ψ 1 (x,y) and ψ 2 (x,y), and propagation constants β1 and β2, respectively. At
Which graph represents the angular velocity as function of time in which the magnitude of angular velocity is contiguously decreasing? Ans) That is down parabola from origin gra
Regard as two charged particles. At a given separation every particle exerts a force of 12 N on the other. What force does every one exert on the other after someone moves the part
Q. What is efficiency of a transformer? Efficiency of a transformer is described as the ratio of output power to the input power. η= output power / input power
What are the advantages of fibers optics? Glass fiber optics are extremely resilient and ideally fine for working in places where the actual conductor will tend to extreme temp
Screw gauge works on the rule of screw. It has a linear scale called as the main scale, and another scale called as the circular scale. The circular scale can be moved by a head sc
velocity of sound is 330m/s and wavelength 1.5 m .With time interval of 1/1000 sec related phase difference will be
How is polymer fibers terminated? PMMA fiber single ends can be of some types always depending upon the nature of the conductor and the last application. A Simply cut fiber wit
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!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd