Final answer:
To find the spring constant, use Hooke's Law with the mass's weight as the force and the stretch length in meters as displacement. The spring constant is 22.4229 N/m for a 0.32-kg mass stretching the spring by 14 cm.
Step-by-step explanation:
To determine the spring constant of the spring when a 0.32-kg mass stretches it by 14 cm, use Hooke's Law, which is represented as F = kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring from its equilibrium position. The force can be found using the weight of the mass (F = mg, where m is the mass and g is the acceleration due to gravity, which is approximately 9.81 m/s2). The displacement needs to be converted to meters from centimeters by dividing by 100.
So, for a mass (m) of 0.32 kg, and a displacement (x) of 0.14 meters, the force (F) is 0.32 kg × 9.81 m/s2 = 3.1392 N. The spring constant (k) is then calculated as k = F/x which gives k = 3.1392 N / 0.14 m = 22.4229 N/m. Therefore, the spring constant of the spring is 22.4229 N/m.