The size or strength of a force refers to its
a. power
b. energy
c. direction
d. magnitude

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.

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

What can you increase the strength of an electromagnet by