Final answer:
To find the proportionality constant k, use Hooke's Law and apply the equation F = kx. For two rubber bands in parallel, the stretch is less than 3 cm; in series, the stretch is 6 cm.
Step-by-step explanation:
To measure the proportionality constant k of a rubber band, you can use Hooke's Law which states that the force (F) applied to stretch or compress a spring by a distance (x) is proportional to that distance, represented as F = kx. Given that a rubber band stretched 3 cm when a 100-g mass was attached, we can first calculate the force exerted by the mass as weight, which is mg (where m is mass and g is the acceleration due to gravity). Assuming g is approximately 10 m/s², the weight would be 1 N (since 100 g is 0.1 kg and 0.1 kg * 10 m/s² = 1 N).
If we have two rubber bands and attach a 100-g mass:
- In parallel, each rubber band will experience half the force, so each will stretch less than 3 cm. Since the total force is unchanged, the parallel combination behaves like a stiffer rubber band with a higher effective spring constant, and as such, the stretch will be less than 3 cm.
- In series, the two rubber bands will stretch a total of twice the original stretch if they are identical because the same weight is pulling through both, so the stretch will be a total of 6 cm.