Answer: k = 1163.72 N/m²
Explanation: if the bow obeys hook's law, then force is proportional to extension.
F = ke.
F= Force = 263 N
k = force constant
e = extension = 0.226m
263 = k * 0.226
k = 263/ 0.226
k = 1163.72 N/m²
1163.7N/m
When a force caused by an object is applied to a spring, the spring applies an equal and opposite force to that object. This is evident in Hooke's law which states that the force(F) applied to a spring, either to cause extension or compression, is directly proportional to the length of the extension or compression (x). i.e
F = k x ---------------------(i)
Where k is the proportionality constant called spring constant.
Given;
F = force exerted on the bowstring = 263N
x = length of extension = 0.226m
Substitute these values into equation (i) as follows;
263 = k (0.226)
Solve for k;
k = 263 / 0.226
k = 1163.7N/m
Therefore, the spring constant of the bow is 1163.7N/m
