Final answer:
When a spring is cut into two equal parts, each part will have a spring constant of K/2.
Step-by-step explanation:
When the spring is cut into two equal parts, each part will have a spring constant of K/2. This is because the spring constant is a measure of the stiffness of the spring, and cutting it in half reduces its stiffness by half.
When a spring with a spring constant k is loaded with a mass m, the system exhibits Hooke's Law, F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Cutting the spring into two equal parts does not change the mass m. When one of the halves is loaded with the same mass, the new spring constant, denoted as k', can be determined. Since the two halves are identical, each half bears half the load.
Thus, the new spring constant k' for the loaded half is related to the original spring constant k by the equation k' = 2k. This is because the force exerted by each half is proportional to its own spring constant, and the overall force is the sum of the forces from both halves. Therefore, when one of the halves is loaded with the same mass, the effective spring constant doubles compared to the original undivided spring.