of3 a) What is the angular speed ofthe rod-hoop-block immediately after the collision? Find an algebraic answer in terms ofthe givens. b) Find an algebraic expression for the center of mass of the rod-hoop-block system immediately after the collision in terms ofthe givens. c) What is the maximum height to which the center of mass of the system will rise after the collision? Find an algebraic answer. Problem 3 (30) A man wraps a rope around a solid circular disk of mass M = 1 kg and radius R = 1 m and unwinds the rope without it slipping by applying a constant force F = 1 N, so the disk rolls without slipping on a level surface. a) What is the magnitude ofthe acceleration a of the disk. Give an algebraic and numeric answer. b) What is the magnitude of the frictional force? Given an algebraic and numeric answer. c) What is the value of the coefficient of static friction between disk and floor that is required in order to maintain the rolling condition? Find an algebraic and numeric answer. Problem 4 (25) Three ball bearings of equal masses m have a small detonator placed between them. When the detonator explodes the masses move out in the directions and angles as shown. If the first ball bearing moves 100 meters up the y-axis from the point of the explosion, as shown, what is the distance of the other two ball bearings from the point of the explosion? Find a numeric answer. 9 bgfpts Problem 5 (30) A man wraps a rope around the edge ofa solid circular disk of mass M = 6 kg and radius R = 1 m. He pulls the rope, which does not slip on the disk, with a constant force F = 14 N, in order to raise a block of mass m = 1 kg. a} Find an algebraic expression for the acceleration ofthe block in terms of the givens ofthe problem. b) lfthe man applies the force for 10 seconds, what is the angular speed of the plate? c} How many revolutions does the disk undergo in that time? Find an algebraic and a numeric answer. Problem 6 (30) A planet of mass m orbits inside a spherical gas cloud of radius R and uniform density p. The planet orbits at a distance r R from the clouds center. What is the gravitational force on the planet? d) Explain in a few lucid sentences why flat rotation curves ofgas clouds orbiting a galaxy provide evidence for the existence of dark matter. Problem 7 (25] A person wants to support a stationary mass m = 20 kg using a beam of length L = 6 m and mass M = 5 kg by applying a force to the end of the beam as shown. The beam rests on a point located d = 1 m from the mass m. Find an algebraic and numeric answer forthe force the person must apply to the beam. Problem 1 (30) A person presses a block of mass m into a spring, compressing the spring a distance xm from its equilibrium position. The spring obeys the force law F = ~l