Final answer:
The free length of the spring in question is calculated by using Hooke's Law to find the displacement caused by the initial load and subtracting this displacement from the measured length, resulting in a free length of approximately 1.0027 inches.
Step-by-step explanation:
To find the free length of the spring, we use Hooke's Law:
F = -kx
Where:
- F is the force applied (the initial load),
- k is the spring rate (spring constant),
- x is the displacement of the spring from its free length.
Given the initial load (F) of 4.6516 lbs and a spring rate (k) of 18.8 lbs/in, we can solve for displacement (x):
x = F / k
x = 4.6516 lbs / 18.8 lbs/in
x = 0.2473 in
The free length (L0) of the spring is then the measured length minus the displacement:
L0 = measured length - x
L0 = 1.25 in - 0.2473 in
L0 = 1.0027 in
Therefore, the free length of the spring is approximately 1.0027 inches.