The spring constant k is found using Hooke's Law and is calculated to be 653.33 N/m. This value is obtained by dividing the force exerted by the mass due to gravity by the displacement caused by the mass hanging from the spring.
To calculate the spring constant k, we use Hooke's Law, which states that the force (F) exerted by a spring is equal to the spring constant (k) multiplied by the displacement (x) from its equilibrium position, or F = -kx. In this scenario, the force applied by the 2.0 kg mass due to gravity (its weight) is F = m * g = 2.0 kg * 9.8 m/s2 = 19.6 N. The spring stretches 3 cm (0.03 m) when the mass is hung from it. Therefore, we can rearrange Hooke's Law to solve for k: k = F / x = 19.6 N / 0.03 m.
The spring constant k is calculated to be 653.33 N/m.
So, the spring constant represents how stiff the spring is, with a higher value meaning a stiffer spring. The given problem required an application of Hooke's Law to determine the spring constant k for a particular spring scenario, by measuring the force applied and the resulting stretch length.