An archer pulls her bow string back 0.370 m by exerting a force that increases uniformly from zero to 225 N. What is the equivalent spring constant of the bow?
To find the equivalent spring constant of the bow, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement.
Hooke's Law can be represented as:
F = k * x
Where:
F is the force applied (225 N)
k is the spring constant we want to find
x is the displacement (0.370 m)
Since the force increases uniformly from zero to 225 N, we can find the average force applied by dividing the total force by 2:
Average force = (0 + 225 N) / 2 = 112.5 N
Now we can rearrange Hooke's Law to solve for the spring constant:
k = F / x
k = 112.5 N / 0.370 m
k ≈ 304.05 N/m
Therefore, the equivalent spring constant of the bow is approximately 304.05 N/m.