A heavy particle is placed at the top of a vertical hoop. Calculate the reaction of the hoop on the particle by means of the Lagrange's undetermined multipliers and Lagrange's equations. Find the height at which the particle falls off.

Q: (3) Consider the Hamiltonian given as H = +²+Fâ , where each term has a clear physical meaning. 2m 2…

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Q: force is projected from point A, at distance a from the center of force O, in a direction…

A: Solution: The force and potential energy of the systems are given by the following :…

Q: Q4: a) Calculate: (uz|A*|u6). b) If the Hamiltonian of harmonic oscillator defined as H = ħw + A*A…

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Q: Example 3. Find the continuously differentiable streamfunction (r) of a singularity-free…

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Q: Problem 3 The Lagrangian of a particle in spherical coordinates is given by 1 L(r, 0, 6; 1, 0, 0) =…

A: Step 1:The Lagrangian given for a particle in spherical coordinates is given in question Step 2: The…

Q: Masses m and 2m are joined by a light inextensible string which runs without slipping over a uniform…

A: To solve this problem, we'll start by defining the generalized coordinates and the Lagrangian…

Q: Problem 4: The center of a long frictionless rod is pivoted at the origin, and the rod is forced to…

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Q: Using the formula for Euler-Lagrange EOM, one can find the Lagrangian and the EOM for a mass sliding…

A: Given data, A particle of mass m is sliding on a frictionless inclined plane.

Q: Consider a large solar sail in the form of a square with sides of length e = 100 m that is…

A: Light is nothing but excitation of the electric and the magnetic field in space. It also behaves as…

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Q: what about the scattering parameter and angle?

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Q: Problem 10.10 Consider a central force given by F(r) = -K/r³ with K > 0. Plot the effective…

A: F= -K/r³ We know that, F= -dU/dr     (where U is  potential energy) -K/r³= -dU/dr dU= K(1/r³)dr…

Q: all and the floor are friction-less, the ladder will slide down the wall and along the floor until…

A: A ladder of length L and mass M is leaning against a wall. Assuming the wall and the floor are…

Q: If the kinetic energy T and the potential energy V of a mathematical system are given T = (k+;) i +…

A: The Lagrangian function is given by, L = T - V The Hamiltonian function is given by, Hq, p, t =…

Q: Set up the integrals to find the ycoordinate of the center of mass for a region of density (x;y)…

A: To find the y coordinate of the center of mass for a region of density ρ(x,y) inside the circle x^2…

Q: In the following vibration system, disk 2 rolls on a non-slip part with uniform mass distribution…

A: Given data, Mass of each component = m Spring constant of the spring = k