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Title+Summary	Name	Date
LFM-CM-02 Frictional force Node id: 3301page Question: Is the frictional force a force of constraint? What is the virtual work done by frictional forces? The principle of virtual work and D' Almebert's principle eliminate constraint forces making use of the fact that these forces do no work. What about friction? Is it a force of constraint in this sense? You find discussion of such fine details only in work of masters. See Sommerfeld \(\S\) II.8, p54. Sommerfeld writes: ... we shall talk about the force of friction, which must be sometimes counted among the forces of reaction, sometimes among applied forces. It is a force of reaction if it occurs as static friction; applied force if it occurs as sliding or kinetic friction. Static friction is automatically eliminated by the principle of virtual work; kinetic friction must be introduced as an applied force. An external indication of this is the occurrence of the experimental constant \(\mu\) in the law of sliding friction.	kapoor	22-08-26 12:08:49	n
QM-1(2019) Theory for Tutorial -I Node id: 3063page For Tutorial-I, you need the Postulate 3 of quantum mechanics. Click Go Back to the tutorial page	kapoor	22-08-26 12:08:34	n
[QUE/CM-02033] Bead on a Rotating Parabolic Wire Node id: 3164page A bead of mass \(m\) slides on a frictionless wire under the influence of gravity and the shape of wire is parabolic with axis begin along the vertical upwards. The wire rotates about the its axis, (\(z\)- axis), with constant angular velocity \(\omega\). Take \(z^2= a\rho\) as equation of the parabola. Set up Lagrangian and obtain equations of motion. Obtain the Hamiltonian. Is theHamiltonian equal to energy? Hamiltonian or energy or both areconstants of motion? Panat	kapoor	22-08-26 12:08:19	n
[QUE/CM-02034] Node id: 3165page A mass \(m\) is suspended by a mass-less spring of spring constant \(k\) and un-stretched length\(b\). The suspension point is pulled upwards with constant acceleration \(a_0\). Gravity acts vertically downwards. Find the Lagrangian and Hamiltonian function and write Hamilton's equations of motion. Find also the period of motion. Panat	kapoor	22-08-26 12:08:32	n
LFM/CM-07 :: Eliminating Zero Frequency Modes of Translation and Rotation Node id: 3109page	kapoor	22-08-26 12:08:27	n
CM@HCU :: Tutorial I Node id: 3065page Assistance for Classical Mechanics Tutorial-I Click to go back to the Tutorial Page	kapoor	22-08-26 12:08:18	n
\(\S\S\) 7.3 Q[2] \(\int_0^\infty \frac{x}{x^4+1} dx\) Node id: 1835page	kapoor	22-08-26 11:08:24	n
\(\S\S\) 7.3 Q[9] \(\int_0^\infty \frac{x^2+1}{(x^4+1)^2}dx \) Node id: 1842page	kapoor	22-08-26 11:08:00	n
\(\S\S\) 7.3 Q[11] \(\int_0^\infty \frac{x^4}{x^{2N}+1} dx\) Node id: 1844page	kapoor	22-08-26 11:08:11	n
\(\S\S\) 7.3 Q[12] \( \int_0^\infty \frac{dx}{x^N+1} \) Node id: 1846page	kapoor	22-08-26 11:08:44	n
\(\S\S\) 7.3 Q[13] \(\int_0^\infty \frac{x^{2N}}{x^{2M}+1} \, dx\) Node id: 1848page	kapoor	22-08-26 11:08:15	n
\(\S\S\) 7.3 Q [7] \(\int_0^\infty \frac{x^2\, dx}{x^6+1}\) Node id: 1840page	kapoor	22-08-26 11:08:57	n
\(\S\S\) 7.3 Q[14] \(\int_0^\infty \frac{dx}{(p+qx^2)^N}\) Node id: 1847page	kapoor	22-08-26 11:08:38	n
\(\S\S\) 7.3 Q [8] \(\int_0^\infty \frac{dx}{(x^2+p^2)(x^2+q^2)}\) Node id: 1841page	kapoor	22-08-26 11:08:07	n
\(\S\S\) 7.3 Q[3] \(\int \frac{dx}{x^4+x^2+1}\) Node id: 1836page	kapoor	22-08-26 11:08:51	n
\(\S\S\) 7.3 Q[4] \(\int_{-\infty}^\infty \frac{dx}{(x^2+x+1)^2}\) Node id: 1837page	kapoor	22-08-26 11:08:24	n
\(\S\S\) 7.3 Q[5] \int_{-\infty}^{\infty}\(\frac{(x^2+2)}{(x^4+10x^2+9)}\) Node id: 1838page	kapoor	22-08-26 11:08:10	n
\(\S\S\) 7.3 Q[6] \(\int_0^\infty \frac{(x-2)}{(x^4+10x^2+9)} dx\) Node id: 1839page	kapoor	22-08-26 11:08:26	n
2019-CM-I @ CMI :: Assignments and Group Activity Q-Papers Node id: 3175curated_content	kapoor	22-08-26 10:08:21	n
2019-CM-I @ CMI :: Quiz Papers with Solutions Node id: 3176curated_content	kapoor	22-08-26 10:08:33	n

LFM-CM-02 Frictional force

Question: Is the frictional force a force of constraint? What is the virtual work done by frictional forces?

The principle of virtual work and D' Almebert's principle eliminate constraint forces making use of the fact that these forces do no work. What about friction? Is it a force of constraint in this sense? You find discussion of such fine details only in work of masters. See Sommerfeld \(\S\) II.8, p54.

Sommerfeld writes:
... we shall talk about the force of friction, which must be sometimes counted among the forces of reaction, sometimes among applied forces. It is a force of reaction if it occurs as static friction; applied force if it occurs as sliding or kinetic friction. Static friction is automatically eliminated by the principle of virtual work; kinetic friction must be introduced as an applied force. An external indication of this is the occurrence of the experimental constant \(\mu\) in the law of sliding friction.

kapoor

22-08-26 12:08:49

n

[QUE/CM-02033] Bead on a Rotating Parabolic Wire

Node id: 3164page

A bead of mass \(m\) slides on a frictionless wire under the influence of gravity and the shape of wire is parabolic with axis begin along the vertical upwards. The wire rotates about the its axis, (\(z\)- axis), with constant angular velocity \(\omega\). Take \(z^2= a\rho\) as equation of the parabola.