rmulaUrl":null,"initialIndex":38,"initialQuestionWindow":[{"id":"90cfcaf6-bc80-4016-bc7e-890a020194b4","revisionId":"cd016ce7-897f-407c-8a9e-4dadabaf4936","questionNumber":null,"questionType":"LA","specification":"An engineer is designing a spring-loaded latch release mechanism on a deep-sea research submersible.\n\n![A diagram showing a horizontal tension spring attached to a fixed vertical anchor on the left, with an applied tension force F pulling it to the right.](https://assets.mathsgenie.co.uk/aqa-qb/a4fb75d3-2e32-4eb9-9cfd-c752cc11c5de.png)\n\nThe spring used in the mechanism has a spring constant of $240\\text{ N/m}$.\nDuring standard operation, an applied locking force of $36\\text{ N}$ stretches the spring.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e338e2fe-af1d-4f8b-b55c-12ae0818bc6d","label":null,"content":"Calculate the extension of the spring.\n\nUse an equation from the physics equation sheet.","markscheme":"- Rearranges the equation or substitutes the given values correctly: $36 = 240 \\times e$ or $e = \\frac{36}{240}$ M1\n- Calculates the correct numerical value: $0.15$ A1\n- States the correct unit: $\\text{m}$ B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"hookes_law","label":"Use Hooke's law","steps":[{"type":"text","order":0,"title":"Identify the values","content":"From the question, use $F=36\\,\\text{N}$ and $k=240\\,\\text{N/m}$ in Hooke’s law, $F=ke$.","highlights":[{"text":"The spring used in the mechanism has a spring constant of $240\\text{ N/m}$.","location":"specification"},{"text":"an applied locking force of $36\\text{ N}$ stretches the spring.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=substituted}{36 = 240e}"},{"latex":"\\htmlData{anchor=rearranged}{e = \\frac{36}{240}}"}],"connections":[{"to":"rearranged","from":"substituted","color":"sky","label":"divide both sides by 240"}]},"order":1,"title":"Substitute and rearrange","description":"Substitute the values, then divide both sides by the spring constant. This earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"text":"Therefore, the extension is:"},{"latex":"e = 0.15\\,\\text{m}"}]},"order":2,"title":"Calculate the extension","description":"The unit is metres because the spring constant was given in N/m. Calculating 0.15 earns A1; stating m earns B1."}]}],"generatedAt":"2026-07-22T11:42:58.222Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"953ef71f-90e5-4ad0-9ee1-abba2d6f45ec","revisionId":"79ea1c7d-6aff-467a-b7a0-1c4931a8b443","questionNumber":null,"questionType":"LA","specification":"A force of $5.4\\text{ N}$ is applied to stretch a metal spring.\nThe extension of the spring is $0.09\\text{ m}$.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"05bfaca4-9b88-43fb-982a-c4e47fefc196","label":null,"content":"Calculate the spring constant, $k$, of the spring and state the unit.\n\nUse the equation:\n$$F = k \\times e$$","markscheme":"- Rearranges the equation or substitutes values to give $k = \\frac{5.4}{0.09}$ M1\n- Calculates the value $k = 60$ A1\n- States the unit of the spring constant as $\\text{N/m}$ (or $\\text{N m}^{-1}$) B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"rearrange_hookes_law","label":"Rearrange Hooke's law","steps":[{"type":"text","order":1,"title":"Choose the unknown","content":"The equation is $F = k \\times e$. Here, $k$ is the spring constant, $F$ is the force, and $e$ is the extension.\n\nWe need to make $k$ the subject. Dividing by $e$ undoes the multiplication by $e$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=given-equation}{F=k\\times e}"},{"latex":"\\htmlData{anchor=rearranged-equation}{k=\\frac{F}{e}}"},{"latex":"\\htmlData{an

Forces and springs

Question 20

Forces and springs Questions

Forces and springs

Question 20

Forces and springs Questions