If you run down some stairs and stop, what happens to your kinetic energy and your
initial gravitational potential energy?

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.

When temperature of a substance increases, of its particles increase resulting in more between particles. real world applications of thermal expansion absolute zero (-273 degrees c) is the lowest possible temperature on the kelvin scale. it is a measure of where a substance has no kinetic energy. heat is a process of the . energy flows spontaneously from a object to a until equilibrium is reached. heat is measured in heat is transferred throughis a method of heat transfer that occurs between particles of matter that are in direct contact with each other. are poor conductors that impede / reduce the rate of heat transfer. is a method of heat transfer that occurs in fluids (non-solids) by means of currents. real world application of convectiona method of heat transfer through electromagnetic waves. when energy moves from one object to another inside a closed system, no energy is or in the system in the transaction. systems will spontaneously move to a state of organized energy or high disorder over time called

Because air contracts as it cools, the air pressure inside a freezer is typically lower than on the outside. why do ice cubes inside a freezer tend to shrink over time? a. the ice dissolves oxygen from the air, forming a denser crystalline matrix.b. the ice reacts chemically with carbon dioxide in the air, forming gaseous carbon compounds.c. the ice melts, and then the liquid freezes as ice crystals on the bottom of the freezer.d. the ice sublimes, and then the water vapor deposits as ice crystals on the sides of the freezer.