Springs are machine elements that store mechanical energy when they are stretched, compressed, twisted, or bent. Engineers use them in suspensions, valves, switches, clamps, watches, and safety mechanisms because they can produce predictable forces over repeated motion. A compression spring under load is a clear example: as the plates push inward, the coils move closer together and the spring pushes back.
Understanding spring design helps engineers choose materials, dimensions, and safety factors that prevent failure.
Key Facts
- Hooke's law for a linear spring: F = kx, where F is force, k is spring rate, and x is deflection.
- Elastic potential energy stored in a spring: U = 1/2 kx^2.
- Spring rate from a force versus deflection graph: k = Delta F / Delta x.
- A stiffer spring has a larger k, so it needs more force for the same deflection.
- For a helical compression spring, more active coils usually decrease the spring rate.
- Common spring types include compression, tension, torsion, and leaf springs.
Vocabulary
- Spring rate
- Spring rate is the force required to deflect a spring by one unit of length.
- Deflection
- Deflection is the change in length or angle of a spring from its unloaded position.
- Hooke's law
- Hooke's law states that the force from an ideal spring is proportional to its displacement within the elastic limit.
- Elastic potential energy
- Elastic potential energy is the energy stored in a deformed spring that can be returned as mechanical work.
- Active coils
- Active coils are the coils in a helical spring that deform and contribute to spring motion under load.
Common Mistakes to Avoid
- Using mass instead of force in F = kx is wrong because the spring responds to force, not directly to mass. Convert mass to weight with F = mg when a mass hangs from or compresses a spring.
- Assuming every spring obeys Hooke's law at all loads is wrong because real springs have an elastic limit. Beyond that limit, the spring may permanently deform or fail.
- Forgetting to square the deflection in U = 1/2 kx^2 is wrong because stored energy grows with the square of displacement. Doubling compression stores four times as much energy for the same spring.
- Confusing compression, tension, and torsion loading is wrong because each spring type is designed for a different deformation. A compression spring resists squeezing, a tension spring resists stretching, and a torsion spring resists twisting.
Practice Questions
- 1 A compression spring has k = 800 N/m. How much force is needed to compress it by 0.050 m?
- 2 A spring stores 2.4 J of energy when compressed by 0.080 m. What is its spring rate k?
- 3 Two compression springs are made from the same steel wire and have the same coil diameter, but Spring A has fewer active coils than Spring B. Which spring is likely stiffer, and why?