Hooke S Law

Given that and are perpendicular, the particle is under the influence of two forces. When is removed, the only force acting on the particle is . The acceleration of the particle due to the force is given by Newton's second law: Where: - is the remaining force acting on the particle, - is the mass of the particle. Thus, the acceleration of the particle is .

Step 1: Understanding the Concept:
The effective stiffness or spring constant of a uniform coiled spring depends heavily on its total unstretched natural length.
Specifically, the spring constant is entirely inversely proportional to the original length of the spring material.
Step 2: Key Formula or Approach:
The defining mathematical relationship is , which means the product of the spring constant and its length is always a constant value: .
Step 3: Detailed Explanation:
Let the initial spring constant strictly be and the initial total length be .
When this uniform spring is systematically cut into perfectly equal smaller pieces, the new length of each individual piece naturally becomes .
Using our established inverse relationship , we can directly equate the initial and final states:
Substitute the new reduced length into the equation:
We safely cancel out the common length variable from both sides of the equation:
Rearranging to formally solve for the new spring constant :
Step 4: Final Answer:
The newly determined spring constant of each individual piece is genuinely .