How a Spring Works: Hooke’s Law and Newton’s Third Law Explained
Question:
Remember how a spring works: when you pull on it, it stretches. Newton’s 3rd Law says that the spring pulls back on you too. If you pull the end of the spring in the +x direction with a force F in the +x direction, the spring stretches by an amount x.
You know that the force has only an x-component and hence:
Fx = kx
where:
- Fx = Applied force along +x
- k = Spring constant (force constant)
- x = Extension of the spring from its natural length
Answer:
Understanding Hooke’s Law
Hooke’s Law governs how springs respond to deformation. It states:
Fspring = −kx
The negative sign indicates the spring’s restoring force acts in the direction opposite to the applied displacement. If the spring is stretched in the +x direction, the spring pulls back in the −x direction.
Applied Force and Direction
Suppose you pull on a spring in the +x direction to stretch it. The applied force from your hand is:
Fapplied = +kx
This is the force you exert to stretch the spring. It has only an x-component, and it acts in the positive x-direction.
Newton’s Third Law
Newton’s Third Law states: “For every action, there is an equal and opposite reaction.” So, when you pull the spring with a force F in the +x direction, the spring pulls back on your hand with a force of:
Freaction = −kx
This restoring force is in the −x direction and has the same magnitude as the force you applied.
Component Analysis
Since the motion and deformation are along the x-axis, all forces are aligned in the x-direction. The y-component of the force is zero:
Fy = 0
✅ Summary:
• The applied force in +x direction is F = kx
• The spring resists this force with Fspring = −kx
• This pair of forces perfectly illustrates Newton’s 3rd Law.
• All forces have only x-components; y-components are zero.
• The applied force in +x direction is F = kx
• The spring resists this force with Fspring = −kx
• This pair of forces perfectly illustrates Newton’s 3rd Law.
• All forces have only x-components; y-components are zero.