Final answer:
To find the spring constant (k) and the unloaded length of the spring, one must apply Hooke's Law using the provided displacements and mass values, and then calculate the corresponding forces and spring stretches.
Step-by-step explanation:
To answer this physics question, we can use Hooke's Law, which states that the force F exerted by a spring is proportional to the displacement x from its equilibrium position. The law is usually formulated as F = kx, where k is the spring constant. Given two different displacements and the corresponding masses, we can calculate the spring constant. When a 0.300-kg mass hangs from the spring, causing a length of 0.200 m, the force exerted by the spring (which is equal to the weight of the mass) is F1 = mg = 0.300 kg × 9.81 m/s2 = 2.943 N. When a 1.95-kg mass hangs from the spring, causing a length of 0.750 m, the force is F2 = 1.95 kg × 9.81 m/s2 = 19.1295 N. To find k, we solve the equation k = F/x for each case and equate them to find the value of k. To find the unloaded length of the spring, we can set the force F to zero and solve for x in the equation F = kx.