Show me the steps to solve 13. Consider a solid cylinder of mass and radius sliding without rolling down the smooth inclined face of a wedge of mass that is free to slide without friction on a horizontal plane floor. Use the coordinates shown in the figure. a. How far has the wedge moved by the time the cylinder has descended from rest a vertical distance ? b. Now suppose that the cylinder is free to roll down the wedge without slipping. How far does the wedge move in this case if the cylinder rolls down a vertical distance ? c. In which case does the cylinder reach the bottom faster? How does this depend on the radius of the cylinder?

Show me the steps to solve 13. Consider a solid cylinder of mass and radius sliding without rolling down the smooth inclined face of a wedge of mass that is free to slide without friction on a horizontal plane floor. Use the coordinates shown in the figure. a. How far has the wedge moved by the time the cylinder has descended from rest a vertical distance ? b. Now suppose that the cylinder is free to roll down the wedge without slipping. How far does the wedge move in this case if the cylinder rolls down a vertical distance ? c. In which case does the cylinder reach the bottom faster? How does this depend on the radius of the cylinder?