The system shown in the figure consists of a block of 4.00 mass, which can move on a horizontal surface with a kinetic friction coefficient of 0.30, and which is attached to a spring with a force constate of 200 / by means of an ideal rope, passing through an ideal pulley. The system is initially at rest, with the spring relaxed until suddenly the block is struck to the right, such that instantaneously its speed becomes 178 /. Determine:
The initial mechanical energy of the system.
The velocity of the block when the spring momentarily returns to its relaxed state, after having reached its maximum elongation.

Which graph best represents the relationship between the electric current and the rate at which a magnet is turning inside an electric generator?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

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.