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.
It is the lowest temperature at which a flammable liquid can form an ignitable mixture with air. At this temperature the vapour may cease to burn when the source of incitation is r
what is band gap?
In a pool game a .17kg cue ball traveling at .75 m/s in the plus x direction hits a stationary eight ball. The eight ball moves off with velocity of .25 m/s at an angle of 37 degre
2. The dipole in problem is removed and the space between plates is filled with Cu of conductivity σ (look up the value). (a) Derive an expression for the current density betwee
A parallel plate capacitor has nineteen interleaved plates each 75mm by 75mm separated by mica sheets 0.2mm thick. Assuming the relative permittivity of the mica is 5. Calcu
if length changes then there is change in the time period how to solve these questions regards
Discuss about the term graded index fibre. Graded index fibre: A graded index fibre is diverse from the step index fibre not merely in the core refractive index variation bu
Light with a frequency of 7.5 x 10 14 Hz is able to eject electrons from the metal surface of a photocell that has a threshold frequency of 5.2 x 10 14 Hz. What stopping potentia
The length of a simple pendulum is about 100cm known to have a accuracy of 1mm.Its period of oscillation is 2s determined by measuring the time for 100oscillations using a clock of
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
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