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.
Define Railway Tanker? A long, cylindrical tank is placed on a carriage that is able to slide without friction on. The mass of the empty tanker is M=180 kg at first the tank is
describe the principle, construction and working of Michelson Interferometer.
The greenhouse effect is significant not only on Earth but also on Venus and Mars. The following table summarizes the following basic observations: (A) Using Stefan's equa
law of successive diintegration
A player hits a ball at some angle the ball goes high up in the space the player runs and catches the ball before it hits the ground which of the two has greater displacement?
applications of statically induced emf and dynamically induced emf
Which statement concerning the electric potential of a solid object made out of a perfectly conducting medium is most correct? Answer: It is the electric field which is z
What are solid core fibers? This optics is cylinders made of diverse polymers and encased upon a transparent tube or sheath. As a standard are manufactured in various gauges or
A popular toy on the market some years ago was the water rocket. Water (at 10°C) was loaded into a plastic rocket and pressurized with a hand pump. The rocket was released and woul
HEAD-ON COLLISION: "If the centers of the colliding bodies stay moving along the similar straight line, the collision is said to be head-on collision".
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