rmulaUrl":null,"initialIndex":42,"initialQuestionWindow":[{"id":"ac07fee8-4602-491a-9439-090058519493","revisionId":"f782d752-c641-4199-a34a-7b9514685f7d","questionNumber":null,"questionType":"LA","specification":"A high-precision tension spring in a mechanical throttle linkage is subjected to a calibration test.\n\nA force of $6.3\\text{ N}$ applied to the spring results in an extension of $14\\text{ mm}$.","difficulty":4,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"e1a7e86f-47ec-4d7d-8ada-4a30b2d68c61","label":null,"content":"Determine the spring constant, $k$, of this spring in $\\text{N/m}$.","markscheme":"- Converts the extension from millimetres to metres: $x = 14\\text{ mm} = 0.014\\text{ m}$ M1\n- Recalls and rearranges Hooke's law equation: $F = kx \\implies k = \\frac{F}{x}$ M1\n- Substitutes the values to find $k$: $k = \\frac{6.3}{0.014} = 450\\text{ N/m}$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"hookes_law","label":"Use Hooke's law","steps":[{"type":"text","order":1,"title":"Convert the extension","content":"The extension is given in millimetres, but the required unit for $k$ is $\text{N/m}$. Therefore, write the extension in metres:\n\n$$14\\text{ mm}=0.014\\text{ m}$$\n\nThis conversion earns the first mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"F=\\htmlData{anchor=hookes-product}{kx}"},{"latex":"\\htmlData{anchor=spring-constant}{k}=\\frac{F}{\\htmlData{anchor=extension-divisor}{x}}"}],"highlights":[{"color":"green","style":"box","anchor":"spring-constant"}],"connections":[{"to":"extension-divisor","from":"hookes-product","color":"sky","label":"divide by x"}]},"order":2,"title":"Rearrange Hooke's law","description":"Use Hooke's law: force equals spring constant multiplied by extension. Divide both sides by the extension to make the spring constant the subject. This earns the second mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"k=\\frac{F}{x}"},{"latex":"k=\\htmlData{anchor=substituted-fraction}{\\frac{6.3}{0.014}}"},{"latex":"\\htmlData{anchor=final-answer}{k=450\\ \\mathrm{N/m}}"}],"highlights":[{"color":"green","style":"box","anchor":"final-answer"}],"connections":[{"to":"final-answer","from":"substituted-fraction","color":"green","label":"calculate"}]},"order":3,"title":"Calculate the spring constant","description":"Substitute the force and the extension in metres into the rearranged equation. Include the unit because spring constant is measured in newtons per metre. Correctly substituting 6.3 N and 0.014 m to obtain 450 N/m earns the A1 mark."}]}],"generatedAt":"2026-07-22T12:04:58.644Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ae8d43c3-fded-43ec-9890-ff9de533c4b0","revisionId":"194ff532-d608-456a-9757-df36d817129c","questionNumber":null,"questionType":"LA","specification":"","difficulty":5,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"c8eb90b6-4407-4aba-bba2-d8a58447e06b","label":null,"content":"A different spring is stretched.\n\nThe work done to stretch the spring is $0.27\\text{ J}$.\n\nThe spring constant of the spring is $150\\text{ N/m}$.\n\nCalculate the extension of the spring.","markscheme":"- Recalls and substitutes values into $E_e = \\frac{1}{2} k e^2$ to get $0.27 = 0.5 \\times 150 \\times e^2$ M1\n- Rearranges to find $e^2 = 0.0036$ (or $e = \\sqrt{0.0036}$) M1\n- Calculates the final extension $e = 0.06\\text{ m}$ A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"elastic_energy","label":"Use elastic potential energy","steps":[{"type":"text","order":0,"title":"Choose the energy equation","content":"Stretching a spring stores **elastic potential energy**. The work done becomes this energy, so use\n\n$$E_e=\\frac{1}{2}ke^2$$\n\nwhere $E_e$ is energy in joules, $k$ is the spring constant in

Forces and springs

Question 22

Forces and springs Questions

Forces and springs

Question 22

Forces and springs Questions