iency/questions","formulaUrl":null,"initialIndex":7,"initialQuestionWindow":[{"id":"239b0b71-0e73-4d51-bfbd-2d7e8f2104c6","revisionId":"72a168e3-061d-47ee-8854-8de9952c510a","questionNumber":null,"questionType":"LA","specification":"An electric winch transfers $284\\,000\\text{ J}$ of useful mechanical energy to lift a cargo container in a time of $55\\text{ s}$.\n\n![An electric winch lifting a cargo container](https://assets.mathsgenie.co.uk/aqa-qb/14eafb2a-ed0b-4d86-aaa3-1310f0f6143b.png)","difficulty":3,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"1806dc4d-17c5-4578-b3e4-c40e972bbd7f","label":null,"content":"Calculate the power transferred by the electric winch.\n\nUse the equation:\n$$P = \\frac{E}{t}$$\n\nGive your answer to 2 significant figures.","markscheme":"- Correct substitution of values into the power equation: $\\frac{284\\,000}{55}$ M1\n- Obtains a raw calculated value of $5160$, $5163.6$ or $5164$ A1\n- States the final answer rounded to 2 significant figures with correct units: $5200\\text{ W}$ (or $5.2\\text{ kW}$) A1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"power_calculation","label":"Calculate power","steps":[{"type":"text","order":0,"title":"Identify the quantities","content":"The supplied diagram already shows the winch lifting the container. Power means the **energy transferred each second**.\n\nUse $E=284\\,000\\text{ J}$ and $t=55\\text{ s}$. Both are already in the units needed for the equation.","highlights":[{"text":"transfers $284\\,000\\text{ J}$ of useful mechanical energy","location":"specification"},{"text":"time of $55\\text{ s}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"P=\\frac{E}{t}"},{"latex":"P=\\htmlData{anchor=substituted}{\\frac{284\\,000\\ \\mathrm{J}}{55\\ \\mathrm{s}}}"},{"latex":"P=\\htmlData{anchor=raw_power}{5164\\ \\mathrm{W}}"}],"highlights":[{"color":"green","anchor":"raw_power"}],"connections":[{"to":"raw_power","from":"substituted","color":"sky","label":"calculate"}]},"order":1,"title":"Substitute the values","description":"Put the energy and time into the given equation. This correct substitution earns the first mark. This gives 5164 W, earning the calculation mark."},{"type":"text","order":2,"title":"Round the answer","content":"Round $5164\\,\\mathrm{W}$ to **2 significant figures**. The first two significant digits are $5$ and $1$; the next digit is $6$, so round the $1$ up to $2$.\n\n$$\\boxed{P=5200\\,\\mathrm{W}}$$\n\nThis has the correct unit and is the final-answer mark."}]}],"generatedAt":"2026-07-22T09:27:55.602Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"348f7962-50e1-40bf-b9d6-7fc4aa2e3e9e","revisionId":"fe62bd2e-a643-40cb-85b4-67fbc1f072b8","questionNumber":null,"questionType":"LA","specification":"An automated winch system lifts a theatrical spotlight of weight $160\\text{ N}$ vertically upwards to a ceiling grid. The spotlight is raised through a height of $8.4\\text{ m}$ in a time of $14.0\\text{ s}$ at a constant speed.","difficulty":3,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"3f26103e-aa80-4f71-bea9-bd0656f3a8cb","label":null,"content":"Calculate the useful power, in watts, developed by the winch during this lift.","markscheme":"- Attempts to calculate the work done against gravity as $160 \\times 8.4 = 1344\\text{ J}$ or substitutes directly into the power formula: $\\text{Power} = \\frac{160 \\times 8.4}{14.0}$ M1\n- Obtains $96\\text{ W}$ (or $96\\text{ J/s}$) A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"direct_power_formula","label":"Use the power formula directly","steps":[{"type":"text","order":0,"title":"Identify the measurements","content":"The weight is the lifting force, the vertical height is the distance moved, and the stated time is the duration of

Power and efficiency

Question 8

Power and efficiency Questions

Power and efficiency

Question 8

Power and efficiency Questions