Understanding the Concepts

* Hooke's Law: This law states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. Mathematically, it's expressed as: F = -kx, where:

* F is the force applied

* k is the spring constant

* x is the displacement (stretch or compression)

* Weight: Weight is the force of gravity acting on an object's mass. It's calculated as: W = mg, where:

* W is the weight

* m is the mass

* g is the acceleration due to gravity (approximately 9.8 m/s²)

Solving the Problem

1. Convert units: We need all quantities in standard units (meters and Newtons).

* 12 cm = 0.12 m

2. Apply Hooke's Law: Since the object is hanging at rest, the force of the spring (kx) balances the weight (W) of the object:

* kx = W

3. Substitute values: We know the weight (W = 24 N) and the displacement (x = 0.12 m). We need to find the spring constant (k):

* k * 0.12 m = 24 N

4. Solve for k: Divide both sides by 0.12 m:

* k = 24 N / 0.12 m = 200 N/m

Answer: The spring constant of the spring is 200 N/m.