Final answer:
To determine the spring constant k, one can divide the known force applied to a spring by the displacement caused in the spring from its equilibrium position. The simplest experimental setup for this would involve hanging known masses from a vertical spring and measuring the displacement.
Step-by-step explanation:
The spring constant k can be experimentally determined by measuring how much a spring stretches or compresses under a known force. According to Hooke's Law, the force F exerted by a spring is directly proportional to its displacement x from the equilibrium position, with k being the proportionality constant. Thus, F = -kx. To find k, one can simply divide the force applied to the spring by the distance the spring is compressed or stretched from its equilibrium position. It is important to use a frictionless setup to eliminate extraneous forces and to ensure that the force measurement is solely due to the spring.
To experimentally determine k with the least number of variables, you could use a setup where an object is attached to the spring and allowed to hang vertically. By adding known masses to the object and measuring the displacement from equilibrium, you can calculate k since the force exerted by the masses (due to gravity) is known. This requires just the measurements of the displacement and the mass.