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.
The velocity of a body was noted to be constant during five minutes of its motion. What was acceleration during this interval its? As velocity of body remains same during given
A satellite of mass "M" is in orbit around the earth. If a second satellite of mass "2M" is to be placed in the same orbit, the second satellite must have a velocity which is:
Draw and explain V-I characteristics of constant voltage and constant current sources. Ans: V-I Characteristics of Constant Voltage Source: A voltage source that has very low
Out of ordinary and extra-ordinary waves, which wave obeys Snell's law?
Physical arrangement of resistors: Before we look at some problems it is necessary to warn you that physical appearances can be deceptive. When components are mounted they are
What is the position vector of point c in equilateral triangle?
(1) Standing pulse can be longitudinal / transverse. (2) The disturbance confined to a particular part among the starting point and reflecting point of the ray. (3) There is
..
Define Surface Contaminations (Wisconsin-Madison)? A surface scientist wishes to remain an exposed surface "clean" (≤ 0.05 adsorbed monolayer) for an experiment lasting for tim
What is the meaning of Refraction? Waves that do not reflect back from a boundary but travel into the new medium instead are said to refract. In one dimension, the wave just mo
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