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.
Q. What is the focal length of a convex lens of focal length 30 cm in contact with a Concave lens of focal length 20 cm ? Is the system a converging or a diverging lens? Ignore
What instrument is used to measure volume? Liquid volume is calculated with beakers, measuring cups, spoons, graduated cylinders, and the like. For regular objects, solid volum
A 10 volt battery connected to a capacitor delivers a charge of 0.5 coulombs. The capacitance of the capacitor is: a) 2 x 10 -2 farads b) 5 x 10 -2 farads c) 2 fa
how
Static limit: The distance through a rotating black hole where no observer can probably remain at rest (w.r.t. the distant stars) due to inertial frame dragging; this region i
What is the fractional change in the resistance of an iron filament when its temperature changes from 25.0°C to 50.0°C?
Q. Give one merit of a scanning electron microscope over a transmission electron microscope? Answer:- The SEM has turn into more popular than the TEM as it can produce ima
UNIFORM ACCELERATION: If velocity of a body alters by equal amounts in equivalent intervals of time, then the body is said to have uniform acceleration. OR If average a
Power ratings of DC Circuit: Electrical equipment can only stand a certain amount of heat production without damage and the safe power which a piece of equipment can consume wi
Inertia on a bicycle Get your bicycle going and then apply the brakes rapidly. View the tendency of your body to stay in motion and pitch you over the handlebars. This is the r
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