A3.0-kg mass moving in the positive x direction with a speed of 10 m/s collides with a 6.0-kg mass initially at rest. after the collision, the speed of the 3.0-kg mass is 8.0 m/s, and its velocity vector makes an angle of 35â° with the positive x axis. what is the magnitude of the velocity of the 6.0-kg mass after the collision?

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.

Using a wheel and axle, a farmer is trying to lift a bucket of water from the bottom of a well. the larger wheel has a radius of 40 cm compared to the axle that has a radius of 10 cm. if a bucket of water is 50 n, then how much effort is required to raise it? 12.5 n 200 n 2 n 500 n

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)