A40 kg crate is pushed across a floor by a force of 10 n at an angle of 35° above the horizontal. determine the normal force exerted by the floor on the crate.

Which of the following represents an upside-down image? o a. +doo b. -doo c. +mo d.-m

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.

If it takes a planet 2.8 x 10^8 s to orbit a star with a mass of 6.2 x 10^30 kg what is the average distance between the planet and the star