Final answer:
The spring constant (k) is calculated using the formula F = kx. The force applied by the 2.60 kg mass is its weight, and when plugged into the formula along with the displacement of 2.26 cm, we find that k = 1128.76 N/m.
Step-by-step explanation:
To calculate the spring constant (k) for a spring that obeys Hooke's law, we can use the formula F = kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position. The force applied by the mass is equal to the weight of the object, which is the mass (m) times the acceleration due to gravity (g). Here, the mass m = 2.60 kg and g ≈ 9.81 m/s2, so F = mg = 2.60 kg × 9.81 m/s2 = 25.506 N. The displacement x given is 2.26 cm, which we convert to meters: x = 0.0226 m. Plugging the values into the formula gives us k = F / x = 25.506 N / 0.0226 m = 1128.76 N/m.