Nitrogen (n2) initially at 40°f and 14.7 lbf/in.2 fills a closed, rigid, 6.5-ft3 tank fitted with a paddle wheel. during a process, the paddle wheel provides 5 btu of energy transfer by work to the gas. the gas temperature reaches 80°f at the end of the process. assuming ideal gas behavior, determine the mass of nitrogen, in lb, and the heat transfer, in btu. kinetic and potential energy effects can be ignored.

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.

What is the weight of a 8-kg substance in n, kn, kg·m/s2, kgf, lbm·ft/s2, and lbf?

The horizontal blue line through the middle of the lens is called the optical axis. as the lamp is moved above or below the axis, keeping the horizontal distance to the center of the lens constant, how does the horizontal distance from the lens to the image change?