Final answer:
The spring constant can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement. In this case, the spring stretches by 2.0 cm when a 500 g mass is hung from it. Plugging the values into Hooke's Law, the spring constant is determined to be 245 N/m.
Step-by-step explanation:
In order to determine the spring constant, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
The formula for Hooke's Law is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.
In this case, the displacement of the spring is 2.0 cm (or 0.02 m) when a 500 g mass is hung from it. The mass can be converted to kilograms by dividing by 1000, so the mass is 0.5 kg.
Plugging these values into the formula, we get:
F = -kx
mg = -kx
0.5 * 9.8 = -k * 0.02
4.9 = -0.02k
k = -4.9 / 0.02
k = -245 N/m
However, since a negative value for the spring constant doesn't make physical sense, we can take the absolute value of k to get the final answer:
The spring constant is 245 N/m.