In preparing to shoot an arrow, an archer pulls a bowstring back 0.43 m by exerting a force that increases uniformly from 0 to 268 N. What is the equivalent spring constant of the bow?

N/m

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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 of the spring from its equilibrium position.

Hooke's Law can be expressed as: F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.

In this case, when the archer pulls the bowstring back, it can be treated as a spring being stretched. The force exerted by the archer increases uniformly from 0 to 268 N, and the displacement is given as 0.43 m.

So, we can use the formula mentioned earlier to find the spring constant:

268 N = -k * 0.43 m

To isolate k, we divide both sides of the equation by -0.43 m:
k = - 268 N / (-0.43 m)

Simplifying the equation:
k = 268 N / 0.43 m

Therefore, the equivalent spring constant of the bow is approximately 623.26 N/m.