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.
How much does automotive oil weigh? As rough guide engine oil generally weighs about 0.87 kg/litre or about 7.2 pounds per US gallon unfortunately a rough answer is the best th
describe optical fiber communication with block diagram
pedaling cycle is less friction or more
Q. Situation of the converging lens - Principle Ray 1? Principle Ray I . The easy one just as in the case of the converging lens this ray goes straight through the centre of t
What is the difference between vibration and waves?
At a distance of 4,000 ft from the launch site, a spectator is observing a rocket being launched. If the rocket lifts off vertically and is rising at a speed of 600 ft/sec when it
baryon decay The idea, predicted through several grand-unified theories, that class of subatomic elements called baryons (of which the nucleons protons & neutrons are members
Q. Explain with the help of diagram and experiment arrangement to produce Newton's rings.
Q State Faraday's laws of electromagnetic induction. First law At any time the amount of magnetic flux linked with a closed circuit changes an emf is induced in the circu
As a 10 kilogram mass on the end of a spring passes through its equilibrium position, the kinetic energy of the mass is 20 joules. The speed of the mass is: a) 2.0 meters per
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