2.5.3 A particle is constrained to move on a vertical weightless circle of radius a in...
3) A particle of mass m is constrained to move on the inside surface of a smooth cone of half- angle a. The particle is subject to a gravitational force. Determine a set of generalized coordinates and determine the constrains. Find Lagrange's equations of motion
4. A particle of mass m is constrained to slide without friction on the surface of a smooth circular bowl of mass M with inner radius R as shown in the figure. The bottom of the bowl lies on a horizontal table and is free to slide without friction along the table. All motion is constrained to the plane of the page. Assume uniform gravitati acceleration. =T-V- State the Lagrangian for this system. Derive the differential equations of motion for...
plz help. thnx The state of a quantum mechanical particle, constrained to move on a circle of radius R in the x-y plane, is given by 4. where ф is the angle that the position vector makes with the x-axis a) Find a value of N which makes the above state normalized b) If Lz is measured, what are the possible outcomes and their corresponding probabilities?
a) What is Schrodinger's equation for a particle of mass m that is constrained to move in a circle of radius R, so that psi depends only on phi? b) Solve this equation for psi and evaluate the normalization constant. (Hint: review the solution of Schrodinger's equation for the hydrogen atom) c) Find the possible energies of the particle. d)Find the possible angular momenta of the particle.
A particle (mass m, charge q) is constrained to move freely along a straight horizontal wire of length L. At one end of the wire is a fixed point charge Q1; at the other end of the wire is a fixed point charge Q2. Assume all three charges are negative, and that Q1 = 4Q2. Determine the particle
A rod of length 2a is constrained to move with its ends on the perimeter of a circle of radius . This circle lies in the horizontal plane and is fixed. A small insect whose mass is equal to that of the rod moves along the rod, starting from its mid-point and maintaining a constant relative speed V, then show that in time t, the rod will turn through an angle 2 V3 We were unable to transcribe this image...
A particle rotates in a circle of radius 4.60 m . At a particular instant its acceleration is 1.30 m/s^2 in a direction that makes an angle of 38.0 degrees to its direction of motion. A) Determine its speed at this moment (m/s) B) Determine its speed 2.20 s later, assuming constant tangential acceleration (m/s)
A particle object undergoes uniform circular motion at a speed v around a circle of radius r. Given v and r, the magnitude of centripetal acceleration is a0. Assume when either v or r are changed, the particle remains in uniform circular motion. 1. Suppose the radius of the circle is cut in half. What happens to the magnitude of the centripetal acceleration? choices: the acceleration doubles, acceleration increases by square root of 2, acceleration remains the same, acceleration decreases...
In the figure, a particle moves along a circle in a region of uniform magnetic field of magnitude B = 4.9 mT. The particle is either a proton or an electron (you must decide which). It experiences a magnetic force of magnitude 3.0 × 10-15 N. What are (a) the particle's speed, (b) the radius of the circle, and (c) the period of the motion? OB
In the figure, a particle moves along a circle in a region of uniform magnetic field of magnitude B = 5.0 mT. The particle is either a proton or an electron (you must decide which). It experiences a magnetic force of magnitude 2.9 × 10-15 N. What are (a) the particle's speed, (b) the radius of the circle, and (c) the period of the motion? OB