The earth's orbit around the sun is very nearly circular, with an average radius of 1.5 x 1011 m. Assume the mass of the earth is 6 x 1024 kg and the mass of the sun is 1.99×1030kg. Determine the average speed of the earth in its orbit around the sun.

How much force must a locomotive exert on a 12840-kg boxcar to make it accelerate forward at 0.490 m/s2?

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 scientific definition of energy that relates to work