A-LevelMathematicsMechanics9709/42 · Feb/Mar 2022 · Q14 Marks

A crane is used to raise a block of mass 600kg vertically upwards at a constant speed through a height of 15 m. There is a resistance to the motion of the block, which the crane does 10000J of work to overcome.

(a)Find the total work done by the crane.[2]
(b)Given that the average power exerted by the crane is 12.5kW, find the total time for which the block is in motion.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

[M1] 600g × 15 [= 90 000] (Attempt potential energy.)
[A1] Total work done by crane [90 000 + 10 000 =] 100 000 J
[M1] 100 000 = 12 500 × t (Use of work done = power × time to set up an equation from which t can be found.)
[A1 FT] Time = 8 s (FT on their work done = 100 000)

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Feb/Mar 2022 Paper 4 Variant 2, question 1.

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