The distance a spring stretches varies directly as the amount of weight that is hanging on it. a weight of 2.5 pounds stretches a spring 18 inches. find the stretch of the spring when a weight of 6.4 pounds is hanging on it.

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.

Sort the images based on whether there's a force of attraction or repulsion between the magnets shown. attraction repulsion

Scientific models are based on current knowledge, which can limit their effectiveness when new discoveries are made.