Free moving particle with mass m (three degrees of freedom); (b) particle with mass m moving in the gravitational field at the surface of the earth: vertical motion of a falling object (one degree of freedom); (c) particle with mass m moving in the gravitational field at the surface of the earth: motion of a projectile (two degrees of freedom). 3. derive euler-lagrange equations (ele) for the three mechanical systems (a, b, and c) in the previous problem 2.

Ammonia enters the expansion valve of a refrigeration system at a pressure of 10 bar and a temperature of 18oc and exits at 6.0 bar. the refrigerant undergoes a throttling process. determine the temperature, in oc, and the quality of the refrigerant at the exit of the expansion valve.

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?

What is the moment of inertia i of this assembly about the axis through which it is pivoted? express the moment of inertia in terms of mr