1. In the block-spring arrangement shown, the x U lilm-k block's mass is 4.00 kg and the spring's constant is 500 me. The block is released from the position xi=0.300m. What are (a) the block's speed at x=0, (b) the work done by the spring 11:0, (0) the A .v instantaneous power due to the spring at the release I } point xi, (d) the instantaneous power at x=0, and (e) the block's position when the power is maximum? (Assume no friction.) :lltnt'lu'tl It) spring \\\\\\ 2. In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball moves a 3.50 m/s along a line making an angle of 22.0 with the cue ball's original direction of motion, and the second ball has a speed of 2.00 ms. Find (a) the angle between the direction of motion of the second ball and the original direction of motion of the cue ball and (b) the original speed of the cue ball. (c) Is kinetic energy of the system conserved? (Show) 3. In the gure, two particles are launched from the origin of the coordinate system at time t=0. Particle 1 of mass m1 = 5.00g is shot directly along the x axis on the frictionless oor, with constant speed 10.0mfs. Particle 2 of mass m; = 3.00g is shot with a velocity of magnitude 20.0 mjs, at an upward angle such that it always stays directly above particle 1. (a) What is the maximum height Hmax reached by the center of mass of the two particle system? In unit-vector notation, what are the (b) velocity and (c) acceleration of the center of mass when the center of mass reaches Hmax? 4. A wheel, starting from rest, rotates with a constant angular acceleration of 2.00 rad/s2. During a certain interval, it turns through 90.0 rad. (a) What is the angular velocity when the wheel at the start of the 3.00s interval? (b) How long has the wheel been turning before the start of the 3.00 interval