Final answer:
The unit rate for a spring's stretch is found by dividing the stretch in millimeters by the weight in grams. With two similar rubber bands, the stretch would be 1.5 cm each in parallel but 6 cm in series when supporting the same mass.
Step-by-step explanation:
The stretch of a spring is proportional to the weight attached to it, which is described by Hooke's Law. To find the unit rate, you must determine how much the spring stretches per unit of weight (grams). In this case, if a spring stretches 3mm for every 100g, then the unit rate is 3mm per 100g, which simplifies to 0.03 millimeters per gram or 30 millimeters per kilogram.
For two similar rubber bands attached to the same mass, if put in parallel, each rubber band would only need to stretch half as much to support the mass, because the load is shared equally between them. So, each would stretch 1.5 cm under a 100g mass. However, if the rubber bands are placed in series, they effectively form one longer rubber band with the same stiffness, and the system would stretch 6 cm under a 100g mass, since each rubber band would stretch the same 3 cm.