A simple model for a pouncing cat is a mass that follows a curved trajectory after being launched from a spring. Imagine a 0.057 kg mass launched by a spring. The spring has a spring constant 3,775 N/m. The mass is launched at an angle of 9 degrees above horizontal. The spring is initially compressed a distance of 24.5 mm. At the peak of its trajectory, the speed of the mass is 1.4 m/s. What is the increase in height (in units of m) of the mass at the peak of its trajectory

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.

Ineed asap! list 3 examples in which friction us or makes things easier in our daily life. explain the effect of friction for each. *make sure you explain the effect of friction for each example! *

If a balloon is taken outside on a very cold day, what will occur?