For a spring with spring constant k, the force to be applied to alter its length when it is either compressed or elongated by a distance x from the equilibrium position is given by F = kx. The force has to be applied in the direction in which the spring...

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For a spring with spring constant k, the force to be applied to alter its length when it is either compressed or elongated by a distance x from the equilibrium position is given by F = kx. The force has to be applied in the direction in which the spring has to be moved.

The archer pulls a bow string back 0.304 m by exerting a force that increases uniformly from 0 to 221 N. At a displacement of 0.304 the force required to pull the string back further is 221 N. The equivalent spring constant of the bow can be calculated as 221 = k*0.304

=> k = 726 N/m

The equivalent spring constant of the bow is 726 N/m