Springs
A spring stretches in proportion to its load. Mechanical aptitude tests ask how far it stretches, and what two or three springs do together. Can you tell?
How far do the springs stretch?
Nine rules are all it takes. Read on, then try the test.
Where it appears
Questions about springs and weights belong to mechanical reasoning (or mechanical comprehension) tests, beside the gears, levers and pulleys. Each shows a picture and asks what happens next. You will meet them in:
Those tests usually give a picture with no numbers to count and no time to spare. Here every picture carries its numbers, so each answer is exact, and the questions grow harder as you get better. It trains the habit those questions reward: find the load each spring carries, then the stiffness it has.
One spring: four rules
Every spring shows its stiffness in newtons per centimetre (N/cm): the load that stretches it 1 cm. The weight hanging from it is in newtons (N). The question is how far it stretches, what load gives a stretch, how long it is with the load on, or which of four springs stretches most.
1Stretch = load ÷ stiffness
A 5 N/cm spring needs 5 N for every centimetre, so a 30 N load stretches it six of them.
stretch = load ÷ stiffness2Twice the load, twice the stretch
When the stiffness is not given, a first stretch gives it: load ÷ stretch. Or keep the ratio: a load one and a half times as big stretches the same spring one and a half times as far. The same idea turns a stretch back into the load that caused it.
stiffness = load ÷ stretch3The length is the spring's own length plus the stretch
A spring that is 15 cm long with nothing on it is longer when loaded. Work out the stretch first, then add it to the unloaded length.
4Which of four stretches most?
Do not guess from the picture: work out every spring's stretch with rule 1, then pick the biggest. The same goes for which ends up longest, where each spring's own length is added in first.
Springs together: five rules
Springs can hang side by side, sharing a load, or one below another, each carrying it. Look at where the weight hangs and which springs it pulls on. The question is how far they stretch together.
5Side by side: the stiffnesses add
Two springs side by side share the load, so together they are a stiffer spring. Add their stiffnesses, then divide the load by the total. Identical springs side by side stretch only 1/2 (or 1/3 ...) as far as one on its own.
stiffness = k + k6One below another: the stretches add
Each spring carries the whole load, so each stretches on its own, and the two stretches add. Identical springs one below another stretch twice (or three times) as far as one.
stretch = load ÷ k + load ÷ k7A chain: each spring carries what hangs below it
With a weight at every joint, the top spring carries all the weights under it, and the lower spring only the one beneath it. Work out each spring's own load first, then each stretch, then add.
8A network: work from the inside out
A network mixes the two arrangements: a pair of springs and a third. Turn the pair into one spring first. Side by side, its stiffness is the two added (rule 5); one below another, their stretches add (rule 6), so its stiffness is 1 ÷ (1 ÷ k + 1 ÷ k). Then join that one spring to the third as the picture shows. A question may also ask which of four arrangements stretches least: work out each one's stretch the same way.
9A beam on two springs: the nearer spring carries more
A light beam hangs from two springs, with a weight placed along it. The weight is shared like a lever's: each spring carries the weight times the distance from the weight to the other spring, over the length of the beam. Then each spring stretches by its own share divided by its own stiffness.
Two questions, solved
1A question about one spring each
Which spring stretches the most?
Try it first, then open the answer.
Show the answer: spring A
- Work out every spring's stretch: the weight over the stiffness.
- A: 78 ÷ 6 = 13 cm.
- B: 4 ÷ 2 = 2 cm.
- C: 90 ÷ 10 = 9 cm.
- D: 12 ÷ 3 = 4 cm.
- A stretches most, 13 cm. The traps: C has the heaviest weight and B the softest spring, but neither stretches most.
The other options, and the slip each one is:
2A question about springs together
How far do the springs stretch?
Try it first, then open the answer.
Show the answer: 36 cm
- The pair side by side: 2 + 6 = 8 N/cm
- One below another: 96 ÷ 8 + 96 ÷ 4 = 12 + 24 = 36 cm
The other options, and the slip each one is:
How the practice test runs
- 3:00 on the clock, and it only runs while a question is on screen.
- Levels: each question is about one spring or about several together, drawn half and half. One spring climbs from a stretch under a second load, to the load for a stretch, the stretch from a stiffness, the length with the load on, which of four stretches most, how much further a soft spring stretches than a stiff one, and which of four ends up longest. Several springs climb from identical springs side by side or in line, to two different ones side by side, two in line, a chain with a weight at every joint, a pair above a third, which of four arrangements stretches least, and a beam hung from two springs.
- The ladder: until your first miss, every right answer jumps a whole level; after it, three right answers in a row jump a level and a miss drops one. Your level carries over to your next session.
- Scoring: a right answer earns the question's points (harder questions pay more), a wrong one costs half as many, so guessing does not pay.
- Every question is new, and the review after a session works every answer out on its picture and names the slip behind each wrong option.
Try the Springs test
Free and adaptive, no account needed. Start with one spring and climb to chains, networks and a beam on two springs.
Start the Springs test