You have been asked to design a machine to move a large cable spool up a factory ramp in 30 seconds. the spool is made of two 2 m diameter disks of wood with iron rims connected together at their centers by a solid cylinder 30 cm wide and 1 m long. sometime later in the manufacturing process, cable will be wound around the cylinder. for now the cylinder is bare but the spool still has a mass of 100 kg. your plan is to attach a thin ring around the cylinder and pull the spool up the ramp with a rope attached to the top of this ring (think of it like a giant yo-yo). the spool will then roll without slipping up the ramp on its two outside disks at a constant speed. to finish the design you need to calculate how strong the rope must be to pull the spool when it is moving up the ramp at a constant speed. the ramp has an angle of 27◦ from the horizontal and the rope will be parallel to the ramp. a set of light weight bearings minimizes the friction between the ring and the cylinder and fixes the orientation of the ring so that the rope always pulls from its top. the diameter of the ring is essentially the same as that of the cylinder.