It takes 1200 J of work to stretch a spring from its natural length of 1 m to a length of 6 m . Find the force constant of the spring. The spring's force constant is \( \square \mathrm{N} / \mathrm{m} \). (Type an integer or a simplified fraction.)

To find the spring constant \( k \), you can use the work done on the spring formula: \[ W = \frac{1}{2} k x^2 \] where \( W \) is the work done, \( k \) is the spring constant, and \( x \) is the extension of the spring. The extension \( x \) here is \( 6 \, \text{m} - 1 \, \text{m} = 5 \, \text{m} \). By substituting the values, we have: \[ 1200 = \frac{1}{2} k (5^2) \] \[ 1200 = \frac{1}{2} k (25) \] \[ 1200 = 12.5k \] \[ k = \frac{1200}{12.5} = 96 \] Therefore, the spring's force constant is \( 96 \, \text{N/m} \).