# In preparing to shoot an arrow, an archer pulls a bow string back 0.304 m by exerting a force that . . . increases uniformly from 0 to 221 N. What is the equivalent spring constant of the bow?...

In preparing to shoot an arrow, an archer pulls a bow string back 0.304 m by exerting a force that . . .

increases uniformly from 0 to 221 N.

What is the equivalent spring constant of the bow?

Answer in units of N/m

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### 1 Answer

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