To determine the force needed to stretch a spring, we use Hooke's Law. Hooke's Law states that the force [tex]\( F \)[/tex] required to stretch or compress a spring by a distance [tex]\( x \)[/tex] (displacement) is directly proportional to that distance.
The formula for Hooke's Law is:
[tex]\[ F = k \cdot x \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied,
- [tex]\( k \)[/tex] is the spring constant, and
- [tex]\( x \)[/tex] is the displacement of the spring.
In this problem:
- The spring constant [tex]\( k \)[/tex] is given as [tex]\( 8.5 \, \text{N/m} \)[/tex].
- The displacement [tex]\( x \)[/tex] is given as [tex]\( 1.2 \, \text{m} \)[/tex].
Using the formula, we can substitute the given values:
[tex]\[ F = 8.5 \, \text{N/m} \times 1.2 \, \text{m} \][/tex]
After performing the multiplication:
[tex]\[ F = 10.2 \, \text{N} \][/tex]
Therefore, the force needed to stretch the spring 1.2 meters is [tex]\( 10.2 \, \text{N} \)[/tex]. The correct answer is:
[tex]\[ \boxed{10.2 \, \text{N}} \][/tex]
