Final answer:
The force constant of the spring is calculated using Hooke's Law and the known stretch from two different loads. To find the unloaded length of the spring, one should extrapolate the data to a point where no external force is applied to the spring.
Step-by-step explanation:
To calculate the force constant of the spring, we use Hooke's Law, which states that the force F exerted by a spring is directly proportional to the displacement x, i.e., F = -kx, where k is the force constant.
From the given information, when a 0.300-kg mass is hung, the spring stretches to 0.200 m, producing a force equal to the weight of the mass (F = mg, with g being the acceleration due to gravity). Hence, k can be calculated for the first mass and corresponding stretch. Similarly, these steps can be applied using the second mass and its stretch to ensure a consistent value for k.
To find the unloaded length of the spring, we need to know the natural length of the spring—its length when no external forces are acting on it. This can be obtained by extrapolating from the two conditions given (loads and subsequent lengths) to the point where the force would be zero.