Question

An unpaved spring has a length of I = 12cm. The load of 5N lasts up to 15cm. How long will the spring be when the load will be 15N? Make a figure.

Answer 1

The spring constant can be determined from the Hook's law:

$$k = \dfrac{F_1}{\Delta l_1} = \dfrac{5N}{15cm - 12cm} = \dfrac53N/cm$$

Then, the expansion under the second force:

$$\Delta l_2 = \dfrac{F_2}{k} = \dfrac{15N}{5/3N/cm} = 9cm$$

Thus, the length of the spring will be:

$$l_2 = 12cm+9cm = 21cm$$

Answer. 21 cm.