Three spin-1/2 particles are fixed in position on the vertices of an equilateral triangle. the interaction amongst themselves and with a uniform external magnetic field, b, is described by the hamiltonian where s, i 1,3, are spin operators, and a is a constant (in units of energy/12). (a) obtain the eigenvalues and eigenvectors of h (b) discuss the degeneracies of the spectrum when b-0. (c) discuss the nature of the ground state when a 0 and when a < 0, still for b 0. (d) discuss the effect the magnetic field causes to the degeneracies when it is switched on.

Apulley with a mechanical advantage of 5 will require you to pull times the amount of rope. a. 1/5 b. 5 c. 10 d. 15

A3.9 g aluminum foil ball with a charge of +4.1×10−9 c is suspended on a string in a uniform horizontal e⃗ field. the string deviates to the right and makes an angle of 30∘ with the vertical. part a part complete what information about the e⃗ field can you determine for this situation? what information about the field can you determine for this situation? only the magnitude of e⃗ only the direction of e⃗ both the magnitude and the direction of e⃗ none of the above previous answers correct part b determine the magnitude of the electric field. express your answer with the appropriate units. e e = nothing nothing request answer part c determine the direction of the electric field. determine the direction of the electric field. to the right to the left away from you toward you

Amachinist turns the power on to a grinding wheel, at rest, at time t = 0 s. the wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. the wheel is run at that angular velocity for 40 s and then power is shut off. the wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. in this situation, the time interval of deceleration is closest to: