part one:
a force f~ = fx ˆı + fy ˆ acts on a particle that

undergoes a displacement of ~s = sx ˆı + sy ˆ

where fx = 1 n, fy = −4 n, sx = 1 m, and

sy = 2 m.

find the work done by the force on the

particle.

answer in units of j.

part two:
find the angle between f~ and ~s.
answer in units of ◦

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.

Mechanical energy is when the amount of kinetic and potential energies added together remains the same. conserved created lost

Why does lightning travel from clouds to the ground?