Certainly! To find the spring constant of the spring, we use Hooke's Law. Hooke's Law states that the force [tex]\( F \)[/tex] required to stretch or compress a spring by some distance [tex]\( x \)[/tex] is directly proportional to that distance. Mathematically, it is given by:
[tex]\[ F = k \cdot x \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied to the spring (in Newtons, [tex]\( N \)[/tex]),
- [tex]\( k \)[/tex] is the spring constant (in Newtons per meter, [tex]\( N/m \)[/tex]),
- [tex]\( x \)[/tex] is the extension or compression of the spring (in meters, [tex]\( m \)[/tex]).
We need to find the spring constant [tex]\( k \)[/tex]. Rearrange Hooke's Law to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{F}{x} \][/tex]
In this problem, we are given:
- The force applied to the spring [tex]\( F = p \, N \)[/tex],
- The extension of the spring [tex]\( x = q \, m \)[/tex].
By substituting these values into the equation for [tex]\( k \)[/tex], we get:
[tex]\[ k = \frac{p}{q} \][/tex]
Thus, the expression that represents the spring constant of the spring is:
[tex]\[ \frac{p}{q} \, \text{N/m} \][/tex]
So, the spring constant [tex]\( k \)[/tex] is given by [tex]\( \frac{p}{q} \)[/tex] with the units in Newtons per meter (N/m).
