Mechanical ComprehensionLesson 14 of 18
Springs and Elasticity
Compression and extension, spring constant, and springs in series or parallel.
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Springs are the one component in this subtest that stores energy and gives it back, and the series-against-parallel comparison here is the exact opposite of the one in circuits.
Hooke's law
Force = spring constant x distance stretched.
The spring constant, k, is stiffness, in pounds per inch or newtons per meter. A larger k means a stiffer spring that needs more force for the same stretch.
A spring stretches 2 inches under a 10-pound load. What is its constant?
10 divided by 2 is 5 pounds per inch.
How far does that spring stretch under 35 pounds?
35 divided by 5 is 7 inches.
Stretch is proportional to load, so doubling the weight doubles the stretch, tripling triples it. A question asking what happens to the extension when the load changes wants that proportion, and no constant is needed to answer it.
Compression works identically. A spring squeezed by a force compresses in the same proportion, and coil springs in a vehicle's suspension work that way.
The elastic limit
Up to a point, a spring returns to its original length when the load is removed. That is elastic behavior.
Beyond the elastic limit it does not. It is permanently deformed, and the proportional relationship no longer holds.
A sagging spring has been loaded past its limit at some point, which is the practical version of the question.
Elasticity is a material property, and it is not the same as being soft or stretchy. Steel is highly elastic - it returns precisely to shape - while putty is not elastic at all despite deforming easily. That distinction is asked and the everyday sense of the word misleads.
Series and parallel
| Springs in series (end to end) | Springs in parallel (side by side) | |
|---|---|---|
| Load on each | the full load | shared between them |
| Stretch of each | the same as one alone | half as much |
| Total stretch | adds: twice as much | half as much |
| Combined stiffness | less than one spring | more than one spring |
In series, the whole load passes through every spring, because each hangs from the one above it. Each stretches its full amount and those stretches add, so the assembly stretches twice as far and is softer than a single spring.
In parallel, the load divides between them, so each carries half and stretches half as far. The assembly is stiffer.
Series is softer, parallel is stiffer. That is the opposite of how resistors behave and the same as how capacitors behave, which is worth noticing rather than memorizing separately.
The reason two springs in series stretch twice as far is worth seeing rather than learning. The bottom spring holds the weight, and the top spring holds the bottom spring plus the weight - which is the same force, because the spring's own weight is negligible. So both feel the full load, both stretch fully, and the extensions add up along the length.
Shock absorbers
A spring alone keeps bouncing. Compress it and release it and it oscillates - up, down, up - long after the bump. A shock absorber damps that oscillation by turning the motion into heat in oil, so the vehicle settles after one movement. Worn shock absorbers show up as a vehicle that keeps bouncing after a bump.
Energy in a spring
A stretched or compressed spring stores potential energy, and releases it when it returns.
More stretch stores more energy, and it grows faster than in proportion - doubling the stretch stores four times the energy, because both the force and the distance have doubled.
That is why a longer draw on a bow shoots further and why a more compressed spring fires harder.
Uses: vehicle suspension, valve springs, clutch springs, scales, clocks, mattresses, retractable pens, and anything that has to return to a position on its own.
What you can skip
Across the 23 questions on this topic in our bank:
- Spring constant notation and Hooke's law by name. Hooke is named once. The questions give the rate in pounds per inch and ask you to multiply.
- Spring types by construction. Coil and torsion-bar springs are not asked by name; leaf springs once.
Where people lose points
Thinking springs in series are stiffer. They are softer.
Applying the resistor rules. Springs behave the opposite way.
Thinking elastic means stretchy. Elastic means returning to shape, and steel is more elastic than rubber by that definition.
Expecting proportionality past the elastic limit.
Dividing the load in a series arrangement. Every spring feels the full load.
Confusing the spring constant with the stretch. A big constant means a small stretch.
Work one in under a minute
A single spring stretches 3 inches under a load. Two identical springs are then used, first end to end and then side by side, with the same load. How far does each arrangement stretch?
End to end - in series: 6 inches. Both springs carry the full load and both stretch 3 inches, and the extensions add.
Side by side - in parallel: 1.5 inches. The load splits, so each carries half and stretches half as far, and they move together.
Series doubles, parallel halves, and the figure shows exactly this with a 1-inch reference case.
Where this leads
Stored elastic energy is the same potential energy as a raised load, and spring behavior is what a vehicle's suspension is built on.
Related lessonsReference
- Work, Energy and Power - potential energy stored and released
- Brakes, Suspension and Steering - springs and shocks doing a job
- Materials and Their Properties - elasticity among the other properties
- Parallel Circuits - the same words, the opposite behavior
Practice this topic
Check that this lesson stuck. Answer questions on springs and elasticity only, and see the right answer and why after each one.
Practice Springs and Elasticity questions