Understanding the Concepts

* Hooke's Law: This law states that the force exerted by a spring is proportional to the distance it is stretched or compressed. Mathematically, it's expressed as: F = -kx, where:

* F is the force

* k is the spring constant (a measure of the spring's stiffness)

* x is the displacement from the equilibrium position

* Weight: The weight of an object is the force of gravity acting on it. 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. Calculate the spring constant (k):

* First, convert the stretch distance from cm to meters: 6 cm = 0.06 m.

* Weight of the 4 kg mass: W = (4 kg)(9.8 m/s²) = 39.2 N

* Using Hooke's Law, solve for k: 39.2 N = k * 0.06 m => k = 653.33 N/m

2. Find the mass that stretches the spring 9 cm:

* Convert the new stretch distance to meters: 9 cm = 0.09 m

* Using Hooke's Law again, solve for the force: F = (653.33 N/m) * 0.09 m = 58.8 N

* Since the force is equal to the weight of the object, solve for the mass: 58.8 N = m * 9.8 m/s² => m = 6 kg

Answer: A mass of 6 kg will stretch the spring 9 cm.