Center of Mass ( 4 points ) Learning Objectives: Apply the concept of center of mass. You have a carton filled with a dozen eggs, each of mass m. Initially the center of mass is at the center of the carton, which is also the origin of a coordinate system. Where is the center of mass of the remaining eggs in terms of the egg-to-egg distance d in each of the following situations (neglect the mass of the carton): a) only egg A is removed, b) eggs B and C are removed. B xRotational energy ( 4 points ) Learning Objectives: Apply concepts of energy conservation for rotational motion. A solid cylinder and hollow cylinder with a thin wall roll both on a horizontal plane without slipping. You know only the (translational) velocity VH of the hollow cylinder. Then both cylinders enter a slope, roll upwards, and both reach the same maximum height. What was the original velocity VF of the full cylinder? Look up the moment of inertia of both cylinders.Rotation ( 4 points ) Learning Objectives: Apply the concept of torque and angular acceleration for rotating objects. A rope is connected to a box. The rope passes over a pulley and is wrapped around a cylinder. Cylinder and pulley turn without friction and the rope does not slip on the pulleys surface. The box has a mass of 3.20 kg, the uniform cylinder a mass of 5.00 kg and a radius of 38.0 cm. The pulley has a mass of 1.90 kg and a radius of 20.0 cm. The box is released from rest and descends as the rope unwraps from the cylinder. a) Find the speed of the box when it has fallen 1.80 m. b) If the sizes and masses of the pulley and cylinder were swapped, how would your answer to question (a) change? Explain your reasoning without recalculating. Pulley Cylinder BoxTorque and forces ( 4 points ) Learning Objectives: Apply conditions for static equilibrium to calculate forces. A horizontal beam weighs 15.0 kg and its center of mass is at its center. A barrel hanging off the beam weighs 32.0 kg. Using the given dimensions, find a) the tension in the cable b) the horizontal and vertical components of the force exerted by the beam to the wall. 5.00 m 3.00 m 4.00 m