Energy of a pendulum Gizmo. Activity C 3.

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.

Imagine you work as a consultant, and your daily job involves listening to the constructive criticism of others. as part of your job, you must listen to opposing viewpoints to make important decisions. in this activity, you are a consulting dam engineer. you must make a decision about four different dams; should they be repaired, taken down, or left alone? you will listen to contrasting opinions about what should be done with the dams before you make the final decision. as the consulting dam engineer, what do you decide to do with this dam? explain your reasoning. by making your decision, did you support the opinions of the mayor and/or the dam safety official? why or why not? (site 1)

Which of these statements is true? a. quarks pair with leptons to form protons and neutrons. b. quarks pair with bosons to form photons. c. quarks pair with photons to form protons and neutrons. d. quarks pair with other quarks to form protons and neutrons. e. quarks pair with electrons to form protons.