Physics

To find the natural length of the spring when no force is applied, we can use the information about the lengths under different forces and apply Hooke's Law.

 

Given Data

Length with 12 N force (compressed) = 26 cm

Length with 8 N force (compressed) = 30 cm

 

Let be the natural length of the spring (the length when no force is applied).

 

Calculate the Change in Length

1. The change in length when the force is 12 N:

  

2. The change in length when the force is 8 N:

 

Set Up Equations Based on Hooke's Law

According to Hooke's Law:

 

Where:

is the force applied,

is the spring constant,

is the change in length from the natural length.

 

For the two scenarios, we have:

1. For 12 N:

 

2. For 8 N: