Springs: relate force to extension
Review Hooke’s law, natural length, unit conversion and static balance with full worked examples. No material test or equipment qualification.
This public guide explains one ideal-mechanics topic. Every completed attempt includes all five guides, alongside its correct count and five topic counts. It is not a personal attempt, performance band, percentile or occupational qualification.
Extension is measured from natural length
The spring questions state an ideal linear range. Within that model the restoring-force magnitude is stiffness multiplied by displacement from natural length, not the entire final spring length. Stiffness in N/m tells how many newtons correspond to a metre of extension or compression in the specified linear relation. It does not mean any real spring can safely move a full metre. Identify whether the problem gives mass, force, total length or extension before choosing numbers for the formula.
A fresh calculation in metres and millimetres
Take an ideal spring with stiffness 180 N/m under a steady 9 N stretching force. Its extension is 9/180 = 0.05 m, or 50 mm. Check by multiplying back: 180 × 0.05 = 9 N. If the same force acts on a different ideal spring of stiffness 360 N/m, extension becomes 0.025 m. Doubling stiffness halves extension when force is fixed; it does not double the stretching force in a problem that explicitly holds force constant.
Magnitude and restoring direction differ
The signed form of Hooke’s law includes a minus sign because restoring force opposes displacement from equilibrium in the chosen coordinate description. When a question asks only for magnitude, the relevant answer is positive stiffness times displacement magnitude. Compression does not make the magnitude negative. For a hanging mass at rest, spring force balances weight, so use the specified gravitational acceleration to convert mass into weight before solving for extension. That equilibrium statement is separate from describing how the mass would oscillate after release.
Convert the displacement unit first
A stiffness written in N/m requires displacement in metres for a force in newtons. Convert millimetres by dividing by 1000 and centimetres by dividing by 100. Write the converted number before multiplying, rather than trying to fix an implausible result afterwards. When solving for stiffness, force divided by extension has units N/m; extension divided by force is a different quantity. A back-substitution into force equals stiffness times extension can reveal a reversed division or a thousandfold unit mistake.
Six written tasks are a limited sample
The spring sub-count shows how many of these six original tasks were answered correctly. It does not test tactile control, material selection, fatigue prediction or real component inspection. Equal counts can hide different mistakes, including use of total length, omitted unit conversion or confusion between mass and weight. Review each explanation alongside the question rather than attaching a general ability label to the total. Zero, partial and perfect attempts all display the same full answer explanations and all five topic guides.
Use proportional changes deliberately
Create a fresh hypothetical example with one stiffness and two stated steady forces. Predict the extension ratio before calculating individual extensions. Then hold force fixed and compare two stiffness values. Keep the springs independent unless a problem explicitly introduces a connected arrangement; a pair of independent springs is not automatically a series or parallel system. Say which quantities remain constant each time. This small written discipline makes a proportional explanation clearer than memorising the numerical answer to a repeated item.
A linear model is not a material guarantee
The ideal law applies here because the questions specify that range. It does not establish a real spring’s elastic limit, allowable stress, wear, temperature response or behaviour after a large deformation. The bank neither measures those properties nor gives an operating setting. Its untimed arithmetic also supplies no speed or endurance norm. Treat a worked answer as a check of a stated relation with explicit units. A higher repeat count may partly reflect memory of this fixed form and is not proof of a training effect.