rmulaUrl":null,"initialIndex":13,"initialQuestionWindow":[{"id":"1b727972-1d58-4359-9606-59ba97ef03bb","revisionId":"07b55157-e195-41bf-a4a5-a7c19f897dfd","questionNumber":null,"questionType":"LA","specification":"A spring inside a mountain bike suspension fork has a spring constant of $320 \\text{ N/m}$.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"37675b95-38b3-4409-a98b-a8b7be8eff45","label":null,"content":"Calculate the work done in stretching this spring by $0.15 \\text{ m}$.\n\nState the unit.\n\nUse the equation:\n$$E_e = \\frac{1}{2} k x^2$$","markscheme":"- Substitutes values into the equation: $E_e = 0.5 \\times 320 \\times 0.15^2$ M1\n- Calculates the value of $3.6$ A1\n- States the unit of work done / energy is $\\text{J}$ (or Joules) B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"substitution","label":"Substitute into the equation","steps":[{"type":"text","order":0,"title":"Identify the equation","content":"The equation is given in the question, so use it directly. The spring constant is $k=320\\ \\text{N/m}$ and the extension is $x=0.15\\ \\text{m}$.\n\nThe highlighted wording tells you the quantity to calculate: the elastic energy stored, which is the work done in stretching the spring.","highlights":[{"text":"Calculate the work done in stretching this spring by $0.15 \\text{ m}$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"E_e = \\frac{1}{2}\\,\\htmlData{anchor=k-symbol}{k}\\,\\htmlData{anchor=x-symbol}{x^2}"},{"latex":"E_e = 0.5 \\times \\htmlData{anchor=k-value}{320} \\times \\htmlData{anchor=x-value}{0.15}^2"}],"highlights":[{"color":"sky","style":"box","anchor":"k-value"},{"color":"amber","style":"box","anchor":"x-value"}],"connections":[{"to":"k-value","from":"k-symbol","color":"sky","label":"substitute k"},{"to":"x-value","from":"x-symbol","color":"amber","label":"substitute x"}]},"order":1,"title":"Substitute the values","description":"Replace k with 320 N/m and x with 0.15 m. Writing this substitution earns the M1 mark, even if the arithmetic later slips."},{"type":"hyper_latex","block":{"nodes":[{"latex":"E_e = \\htmlData{anchor=expression}{0.5 \\times 320 \\times 0.15^2}"},{"latex":"E_e = \\htmlData{anchor=answer}{3.6}"},{"text":"Therefore, the work done is 3.6 J. The calculated value earns the A1 mark, and the joule unit earns the B1 mark."}],"highlights":[{"color":"green","style":"box","anchor":"answer"}],"connections":[{"to":"answer","from":"expression","color":"green","label":"calculate"}]},"order":2,"title":"Calculate the energy","description":"Now evaluate the expression to find the work done."}]}],"generatedAt":"2026-07-22T11:09:23.129Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"30259a68-1e93-4534-b209-085e0acc4e9e","revisionId":"b8b7917f-d3b0-4693-8248-3f1eea88fbe9","questionNumber":null,"questionType":"LA","specification":"A student investigates a spring used in a model trampoline.\n\n![A diagram of a model trampoline assembly.](https://assets.mathsgenie.co.uk/aqa-qb/52052baa-7f1f-457f-b9f1-b6947e694019.png)\n\nThe spring has a spring constant of $80\\text{ N/m}$.\nAn applied force of $28\\text{ N}$ stretches the spring.","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"4a13d33c-d0f7-46f4-87ed-6f5b793e15da","label":null,"content":"Calculate the extension of the spring.\n\nUse an equation from the physics equation sheet.","markscheme":"- Substitutes values into $F = k \\times e$ to get $28 = 80 \\times e$, or rearranges the equation to $e = \\frac{28}{80}$ M1\n- Calculates the extension as $0.35$ A1\n- States the correct unit as $\\text{m}$ B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"hookes_law","label":"Use Hooke's law","steps":[{"type":"text","order":0,"title":"Ch

Forces and springs

Question 9

Forces and springs Questions

Forces and springs

Question 9

Forces and springs Questions