answer of $9.8$ A1\n- States the correct unit as $\\text{J}$ (or Joules) B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"elastic_energy","label":"Elastic energy calculation","steps":[{"type":"text","order":1,"title":"Convert the compression","content":"The displacement $x$ must be in metres because the spring constant is in $\text{N/m}$.\n\n$$35\\text{ mm}=\\frac{35}{1000}\\text{ m}=0.035\\text{ m}$$","highlights":[{"text":"$$35 \\text{ mm}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"E_e=\\frac{1}{2}kx^2"},{"latex":"E_e=\\frac{1}{2}\\htmlData{anchor=constant}{\\color{@sky}{(1.6\\times10^4)}}\\htmlData{anchor=compression}{\\color{@orange}{(0.035)}}^2"},{"latex":"E_e=9.8"}],"highlights":[{"color":"sky","style":"text-color","anchor":"constant"},{"color":"orange","style":"text-color","anchor":"compression"}]},"order":2,"title":"Substitute into the equation","description":"M1: convert 35 mm to 0.035 m and substitute it with k = 16000 N/m."},{"type":"text","order":3,"title":"State the work done","content":"The work done **on** the spring becomes elastic potential energy, so the work done is:\n\n$$\\boxed{9.8\\text{ J}}$$\n\nThe correct number earns A1, and stating $\text{J}$ (joules) earns B1.","highlights":[{"text":"State the unit.","location":"specification"}]}]}],"generatedAt":"2026-07-21T15:07:54.189Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"291107c7-461e-4294-9de1-63cc38bdb1b7","revisionId":"cf05adf3-da9b-4cf3-b8df-296efc018c93","questionNumber":null,"questionType":"LA","specification":"Figure 1 shows a plunger mechanism from a toy pinball machine.\n\nThe plunger contains a spring that is compressed before launching a ball.\n\nThe spring constant of this spring is $240 \\text{ N/m}$.\n\n![Figure 1: A schematic diagram of a toy pinball plunger. The diagram shows the spring in its relaxed state and then in its compressed state when pulled back. A label and dimension line indicate that the spring is compressed by a distance of $35 \\text{ mm}$.](https://assets.mathsgenie.co.uk/aqa-qb/1bc0723c-30b9-437d-bb7e-1e23a021554e.png)","difficulty":4,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"181ceabf-652f-4f76-a44e-4a93c62570fb","label":null,"content":"Calculate the force needed to compress the spring by the amount shown in Figure 1.\n\nGive your answer to an appropriate number of significant figures.","markscheme":"- Converts the compression distance from millimetres to metres: $e = 35 \\text{ mm} = 0.035 \\text{ m}$ B1\n- Recalls Hooke's Law $F = ke$ and substitutes the values: $F = 240 \\times 0.035$ M1\n- Calculates the final force as $8.4 \\text{ N}$ to an appropriate 2 significant figures A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"hookes_law","label":"Use Hooke's law","steps":[{"type":"text","order":0,"title":"Identify the extension","content":"The supplied diagram already shows the spring being compressed by $35\\text{ mm}$. In Hooke’s law, the letter $e$ means the change in length of the spring, so here $e$ is the compression distance.\n\nThe spring constant is $k=240\\text{ N/m}$.","highlights":[{"text":"The spring constant of this spring is $240 \\text{ N/m}$.","location":"specification"},{"text":"compressed by a distance of $35 \\text{ mm}$.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"e=\\htmlData{anchor=compression-mm}{35\\ \\mathrm{mm}}"},{"latex":"e=\\htmlData{anchor=compression-m}{0.035\\ \\mathrm{m}}"}],"highlights":[{"color":"green","style":"box","anchor":"compression-m"}],"connections":[{"to":"compression-m","from":"compression-mm","color":"sky","label":"divide by 1000"}]},"order":1,"title":"Convert to metres","description":"The spring constant is measured per metre, so convert the compression before substituting. B1: correctly converting

Forces and springs

Question 3

Forces and springs Questions

Forces and springs

Question 3

Forces and springs Questions