A pendulum is measured to have a max velocity of 2.1 m/s. Determine the height that the pendulum is released from.

Many machines- including inclined planes such as ramps- increase the strength of the force put into the machine but decrease the distance over which the force is applied.

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.

What is required for an electric charge to flow through a wire? zero resistance in the wire a balance of electric potential high resistance in the wire a difference in electric potential