Spin in a magnetic field ((20+20) pts the hamiltonian for a spin s of a particle with charge e in an applied magnetic field b is given by h=-ges-b 2m where g is the gyromagnetic ratio a) calculate ds/dt. b) describe the motion if the magnetic field is in the y direction. express the results in terms of the initial spin components.

1. consider the case in which air fills air shocks on a truck trailer. the pressure in the shocks is 2 mpa. the temperature is 300 k. the diameter of the shock piston is 10 cm and the initial length of the cylindrical cavity containing the compressed air is 40 cm. a. the truck is gradually loaded over a period of a day in a static setting. the temperature is held constant for the atmosphere and thus for the gas shock. calculate the compressibility of the air in the shock for this condition when the truck is initially being loaded. b. if the shocks were loaded in a dynamic setting by driving over bumps, what would be the compressibility? state your assumption. c. what is the initial load on the shock if the shock is in an atmospheric 100 kpa? d. if the shock is compressed using the process described in part a, and the air shock compressed air cavity length decreases to 20 cm, what is the additional load applied to the shock?

The free body diagram shows a box being pulled to the left up a 25-degree incline. the magnitude of the normal force is

What is the magnitude of the acceleration vector which causes a particle to move from velocity −5i−2j m/s to −6i+ 7j m/s in 8 seconds. answer in m/s.