rmulaUrl":null,"initialIndex":14,"initialQuestionWindow":[{"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":"Choose the equation","content":"Use the equation $F = k \\times e$, where $F$ is the applied force, $k$ is the spring constant and $e$ is the extension.","highlights":[{"text":"Use an equation from the physics equation sheet.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=formula}{F=k\\times e}"},{"latex":"\\htmlData{anchor=substitution}{28=80\\times e}"},{"latex":"\\htmlData{anchor=rearranged}{e=\\frac{28}{80}}"}],"highlights":[{"color":"green","style":"box","anchor":"substitution"}],"connections":[{"to":"substitution","from":"formula","color":"sky","label":"substitute values"},{"to":"rearranged","from":"substitution","color":"orange","label":"divide by 80"}]},"order":1,"title":"Substitute the values","description":"This correct substitution earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=fraction}{e=\\frac{28}{80}}"},{"latex":"\\htmlData{anchor=answer}{e=0.35\\ \\mathrm{m}}"}],"highlights":[{"color":"green","style":"box","anchor":"answer"}],"connections":[{"to":"answer","from":"fraction","color":"teal","label":"calculate"}]},"order":2,"title":"Calculate the extension","description":"The calculation earns A1; stating the unit m earns B1."}]}],"generatedAt":"2026-07-22T09:43:02.036Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"307f1555-c01f-4964-8e9a-42948b8eb100","revisionId":"415d0810-eaa6-4e19-9b86-0b0559ece3dc","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"9bc0f839-d434-4045-8f24-e07364f2c9e7","label":null,"content":"The spring constant of a spring is $50\\text{ N/m}$.\n\nThe spring is stretched so that its extension is $8.0\\text{ cm}$.\n\nCalculate the elastic potential energy stored in the spring.\n\nUse the equation:\n\n$$\\text{elastic potential energy} = 0.5 \\times \\text{spring constant} \\times (\\text{extension})^2$$","markscheme":"- Converts the extension to meters: $e = \\frac{8.0}{100} = 0.08\\text{ m}$ M1\n- Substitutes values into the formula to obtain $E_e = 0.16\\text{ J}$ A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"elastic_energy","label":"Calculate elastic energy","steps":[{"type":"text","order":0,"title":"Convert the extension","content":"The equation needs the extension in metres. Convert centimetres to metres by dividing by $100$:\n\n$$e=\\frac{8.0}{100}=0.08\\text{ m}$$\n\nThis conversion earns M1.","highlights":[{"text":"extension is $8.0\\text{ cm}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"E_e=0.5\\times50\\times(0.08)^2"},{"latex":"E_e=0.16\\text{ J}"}]},"order":1,"title":"Substitute and cal

Forces and springs

Question 10

Forces and springs Questions

Forces and springs

Question 10

Forces and springs Questions