In preparing to shoot an arrow, an archer pulls a bowstring back 0.37 m by exerting a force that increases uniformly from 0 to 246 N. What is the equivalent spring constant of the bow?

To find the equivalent spring constant of the bow in this scenario, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law can be written as:

F = k * x

Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.

In this case, we are given that the force increases uniformly from 0 to 246 N as the bowstring is pulled back by 0.37 m.

We can use this information to determine the equivalent spring constant of the bow:

Step 1: Determine the displacement (x) of the bowstring.
Given that the bowstring is pulled back by 0.37 m, we can use x = 0.37 m.

Step 2: Determine the force (F) exerted by the bowstring.
The force increases uniformly from 0 to 246 N. Since the force is increasing uniformly, we can use the average force, which is half of the maximum force, to calculate the spring constant. So, F = (0 + 246 N) / 2 = 123 N.

Step 3: Use Hooke's Law to find the spring constant (k).
We can rearrange Hooke's Law to solve for the spring constant:
k = F / x

Substituting the values we found:
k = 123 N / 0.37 m ≈ 332.43 N/m

Therefore, the equivalent spring constant of the bow is approximately 332.43 N/m.