What is the ratio of the seperation velocity to the approach velocity? And how does the elasticity of the collision relate to this ratio? Thanks in advance

An ideal spring has a spring constant (force constant) of 2500 n/m, is stretched 4.0 cm, how much elastic potential energy does it possess? (a) 3j (b) 0.00j (c) 1j (d) 2j (e) 4j

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.

Kate is working on a project in her tech education class. she plans to assemble a fan motor. which form of energy does the motor convert most of its electric energy into? a. light energy b. motion energy c. sound energy d. thermal energy