Problem 4: (use energy methods) When s = 0, the spring on the firing mechanism is unstretched. If the spring is pulled back to s = 100mm and released. The mass of the ball is 0.3kg. Determine: 1. The speed of the ball as it leaves the spring and is about to start moving on the circular track. 2. The maximum angle θ the ball will travel without loosing contact with the circular track. Assume all contact surfaces to be s

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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.

Calculate the mass of an object that has a momentum of 100kg x m/sec and velocity of 4 m/sec