A particle of mass m is attached to a fixed point in space by a massless rigid rode of length a a...
A particle of mass m is attached to a fixed point in space by a massless rigid rode of length a and can freely rotate about this point. Find the quan- tum energy levels of the system. What is the degeneracy of each energy level (i.e. how many different quantum states have given energy)? Compare to the one of hydrogen atom
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A particle of mass m is attached to a fixed point in space by a massless rigid rode of length a a...
2. Consider a particle of mass M attached to a rigid massless rod of fixed length...
2. Consider a particle of mass M attached to a rigid massless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about its fixed point. (a) Give an argument why the Hamiltonian for the system may be written as 21 21 with/-MR2 (b) If the particle carries charge q, and the rotor is placed in a constant magnetic field B, what is the modified Hamiltonian? (e) What is the energy...
2) A particle of mass m, is attached to a massless rod of length L which...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
A mass m has a massless hook of length 2L attached to it. The end of...
A mass m has a massless hook of length 2L attached to it. The
end of this hook is a massless sticky scoop. This system of mass
and hook is initially at rest. Another mass m flies with speed v1
directly into this scoop, sticks, and the whole thing starts to
move and rotate. Find expressions for the linear and rotational
velocity of the combined object after the first mass is caught.
4. (a) Three point masses are attached to a massless rigid rod. Mass m,-1.0 kg is...
4. (a) Three point masses are attached to a massless rigid rod. Mass m,-1.0 kg is located at x = 1.0 cm, mass m2-2.0 kg at x = 2.0 cm and mass m,-3.0 kg at x-3.0 m. Find the center of mass of the system. (b) Find the center of mass of the four masses as below. mi 2.0 kg at point (1,2) cm; m 3.0 kg at point (2,-3) cm; m -4.0 kg at point (3,-4) cm and m...
a. A particle of mass m moves freely on a line of length a il In...
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs,...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
A rigid bar with mass m and length L is pivoted at the fixed point O....
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
A massless rigid rod whose length L = 21.0 cm has a ball of mass m...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
m D 0.35 m Four point masses are attached together by massless rigid rods. If point...
m D 0.35 m Four point masses are attached together by massless rigid rods. If point mass A is 9.0 kg, point mass B is 2.0 killograms, point mass C is 4.5 kg, and D is 2.5 kg. And masses A and B have the same distance between them as B and C, distance m, 0.3 m. Finally the distance between mass C and D is, distance p, 2.5 m. Find the center of mass of the object from point,...
Calculate the expectation value of the kinetic energy for the particle of mass m on a...
Calculate the expectation value of the kinetic energy for the particle of mass m on a line of length a in a state with quantum number n. Compare your result to the expression for the energy level of the particle and explain any similarities or differences.
2. Consider a particle of mass M attached to a rigid massless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about its fixed point. (a) Give an argument why the Hamiltonian for the system may be written as 21 21 with/-MR2 (b) If the particle carries charge q, and the rotor is placed in a constant magnetic field B, what is the modified Hamiltonian? (e) What is the energy...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
A mass m has a massless hook of length 2L attached to it. The
end of this hook is a massless sticky scoop. This system of mass
and hook is initially at rest. Another mass m flies with speed v1
directly into this scoop, sticks, and the whole thing starts to
move and rotate. Find expressions for the linear and rotational
velocity of the combined object after the first mass is caught.
4. (a) Three point masses are attached to a massless rigid rod. Mass m,-1.0 kg is located at x = 1.0 cm, mass m2-2.0 kg at x = 2.0 cm and mass m,-3.0 kg at x-3.0 m. Find the center of mass of the system. (b) Find the center of mass of the four masses as below. mi 2.0 kg at point (1,2) cm; m 3.0 kg at point (2,-3) cm; m -4.0 kg at point (3,-4) cm and m...
a. A particle of mass m moves freely on a line of length a il In the same diagram, draw the wave function and the squared wave function for the 2nd excited state of the particle. (4 marks) ii. What is the difference between classical and quantum mechanical behavior of the particle in such a box? (3 marks) Hi. Write the expression for the energy of the particle moving freely in a box of sides a, b and c. (2...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
m D 0.35 m Four point masses are attached together by massless rigid rods. If point mass A is 9.0 kg, point mass B is 2.0 killograms, point mass C is 4.5 kg, and D is 2.5 kg. And masses A and B have the same distance between them as B and C, distance m, 0.3 m. Finally the distance between mass C and D is, distance p, 2.5 m. Find the center of mass of the object from point,...
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