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.
What is the raw file size for an image of 80 rows and 100 columns, with pixels on 14 bits and with an extra row for the header? The minimum and maximum values observed in a
A confined quantity of air undergoes two thermodynamic processes departing from an initial equilibrium state where the temperature is 20°C, the absolute pressure is 1bar, and the v
An inductor is generally constructed as a coil of conducting material, characteristically copper wire, wrapped around a core either of air or a ferromagnetic material. Core materia
Write about the main features in which Fresnel and Fraunhoffer approaches of diffraction differ? Mention some (at least four) applications of diffraction.
what will happen if we place a glass with the size of the earth at a distance of 10 light years apart
a rocket is launched at an angle 53 degree to the horizontal with a speed of 100 m/s. it moves along its initial line of motion with an acceleration of 30m/s for 3 seconds. at thi
Interference of waves: When two waves of similar amplitude and period traveling in the similar medium superpose, they reinforce each other at one point and cancel at others. Th
Ceramics are materials made by higher temperature firing treatment of natural clay and certain inorganic matters. Structurally ceramics are crystal bonded together. Other materials
A 5.0-cm-tall object is placed 16 cm from a convex lens with a focal length of 8.4 cm. What are the image height and orientation?
to derive expreation for magnitude & direction for the resultant which two are acting at a point
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