Question

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.)

Answer 1

37.4 cm

Step-by-step explanation:

The force that the spring exterts when stretched is:

`F = -k (x-x_0)`

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:

`-133 N = -680 N/m (0.57m -x_0)`

Solving for x_0

`x_0 = 0.57 m -(133)/(680) m = 0.57 - 0.196 m = 0.374 m`