Final answer:
To determine the total spring constant for two springs in series, the combined stiffness can be calculated with the formula 1/k_total = 1/k_1 + 1/k_2. The most straightforward experimental setup to find the force constant k involves hanging a known mass from the spring and measuring the displacement.
Step-by-step explanation:
A student asked for a model to find the total spring constant k for two springs in series. A simplification can be found considering the force constant of a spring, determined by how much force is needed to compress or stretch the spring a given distance from the equilibrium position. Recognition that when two springs are in series, the same force is applied to both, whereas the distance each spring compresses or stretches may be different. The total distance is the sum of the individual displacements.
To calculate the force constant k for two springs in series, the formula to use is 1/k_total = 1/k_1 + 1/k_2, where k_1 and k_2 are the force constants of the first and second springs, respectively.
For the experiments provided, the one requiring the least number of measurements would involve a simple setup where a mass is hung from the spring, and the displacement due to the mass is measured to find k. For example, an experiment where the length of the spring changes when a known mass is attached allows the determination of the force constant using Hooke's Law, F=kx, where F is the force (equivalent to the weight of the mass), k is the spring constant and x is the displacement.