Final answer:
The force constant of the spring assembly is approximately 286,299.2 N/m. The work required to compress the assembly by the first half inch is approximately 0.2291 J.
Step-by-step explanation:
To find the force constant of the spring assembly, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to its displacement from equilibrium. Using the formula F = kx, where F is the force applied, k is the force constant, and x is the displacement, we can rearrange the equation to solve for k. In this case, the force is 36,340 lb and the displacement is 11 - 6 = 5 inches. Converting the force to Newtons (1 lb = 4.4482 N) and the displacement to meters (1 inch = 0.0254 m), we can calculate the force constant:
F = kx
36,340 lb = k(5 inches)
36,340 lb = k(0.127 m)
k = 36,340 lb / 0.127 m
k ≈ 286,299.2 N/m
b. To find the work required to compress the assembly by the first half inch, we can use the formula for work done on a spring, which is given by W = (1/2)kx^2. In this case, the force constant is 286,299.2 N/m and the displacement is 0.5 inches. Converting the displacement to meters, we can calculate the work:
W = (1/2)kx^2
W = (1/2)(286,299.2 N/m)(0.0127 m)^2
W ≈ 0.2291 J