How much work is required to slow a 20 cm diameter solid ball that has a mass of 2.0 kg from 5.0 m/s to 1.0 m/s?

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.

At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° c. what is the standard deviation of the temperature increase?

Your town is considering building a biodiesel power plant describe at least two advantages and two disadvantages