The lagrangian for a charged particle q of with a velocity v is mass m -43 1 l where the velocity-dependent potential u is specified by the scalar potential vector potential a as and the u q-qa v v. find the canonical momentum p of the particle. a (b) derive the hamiltonian h of the system. remind you that the hamiltonian function must be expressed in terms of the momentum, not the velocity oves in space with a constant magnetic field b such (b x r). assume that 0. show that (c) suppose the charged particle mov that the vector potential is given by a 1 r, 2] and 2m m

An insurance company wants to know if the average speed at which men drive cars is higher than that of women drivers. the company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour. another sample of 18 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a standard deviation of 2.5 miles per hour. assume that the speeds at which all men and all women drive cars on this highway are both approximately normally distributed with unknown and unequal population standard deviations.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Gasoline comes from petroleum, which is made from ancient living things. petroleum, therefore, contains a type of energy. a. heat b. nuclear c. biological d. chemical potential