consider a throw ball to the air ,whre lagragian is given by ,L( m /2+Y^ '2 +Z^' 2 ]- msz, find the two concider momuntum when it is invariant under translation at x&x+E and y&yE(both x and y are cyclic cordinate)

During spring semester at mit, residents of the parallel buildings of the east campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. a balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. assume that the stretching of the hose obeys hooke's law with a spring constant of 89.0 n/m. if the hose is stretched by 5.80 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length? unitst 3 number-1497 the tolerance is +/-5% open show work click if you would like to show work for this question:

Two point charges are on the y axis. a 3.90-µc charge is located at y = 1.25 cm, and a -2.4-µc charge is located at y = −1.80 cm. (a) find the total electric potential at the origin. v (b) find the total electric potential at the point whose coordinates are (1.50 cm, 0). v

Consider an ideal gas at 27.0 degrees celsius and 1.00 atmosphere pressure. imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube. what is the length l of an edge of each small cube if adjacent cubes touch but don't overlap?