Hooke's law:
F = -kx
F is the spring force, k is the spring constant, and x is the displacement of the spring. The negative sign is there to indicate that the force acts in the opposite direction of the displacement (e.g. if you stretch a spring towards the right, you will feel a force pulling towards the left).
Looking at Hooke's law, the magnitude of the force is directly proportional to its displacement; that is to say, if the displacement increases, so does the magnitude of the spring force, and if the magnitude of the force increases, this necessitates an increase in the displacement.
1. As the force on a spring increases, the distance it stretches decreases.
An increase in force necessitates an increase in displacement. This statement is false.
2. As the force on a spring increases, the distance it stretches increases.
An increase in force necessitates an increase in displacement. This statement is true.
3. As the force on a spring increases, the spring's length remains unchanged.
An increase in force necessitates an increase in displacement. This statement is false.
4. The distance a spring stretches has nothing to do with how much force is applied to it.
Hooke's law shows that the spring force and its displacement are very much dependent on each other. This statement is false.
Only statement 2 is true. As the force on a spring increases, the distance it stretches increases.
