Final answer:
The spring constant is calculated using Hooke's Law, which gives a result of 10,000 N/m for the spring when it extends by 10 cm under a force of 1000 N.
Step-by-step explanation:
To find the spring constant (k), we use Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance (x) is proportional to that distance. This is expressed as F = kx. In your case, the spring extends by 10 cm (which is 0.1 meters since we need units in meters for consistency) when a 1000 N force is applied. Therefore, we rearrange the formula to solve for the spring constant k, which gives us k = F / x.
Using the provided numbers, we get k = 1000 N / 0.1 m = 10,000 N/m. So, the spring constant for the spring is 10,000 newtons per meter.