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The stiffness of a particular spring is 680 N/m. One end of the spring is attached to a wall. When you pull on the other end of the spring and hold it stretched with a steady force of 133 N, the spring elongates to a total length of 57 cm. What was the relaxed length of the spring? (Remember to convert to S.I. units.)

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horaciocrotte

Answer:

37.4 cm

Explanation:

The force that the spring  exterts when stretched is:

[tex]F = -k (x-x_0)[/tex]

Where x_0 is the relaxed length and k = 680 N/m

If a steady force of 133 N is applied when pulling the spring and elonged to a total length of 57 cm, the spring must extert the same force, but in the opposite direction, that is:

[tex]-133 N = -680 N/m (0.57m -x_0)[/tex]

Solving for x_0

[tex]x_0 = 0.57 m -\frac{133}{680} m = 0.57 - 0.196 m = 0.374 m[/tex]

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