Question

A crane on a building site lifts bricks of total mass 200kg, initially at rest on the ground, with uniform acceleration.
When the bricks are 5m from the ground, they have a speed of 5m/s.
How much work is done during this process?
A) 2.5kJ
B) 10kJ
C) 12.5kJ
D) 35kJ​​

Answer 1

Answer:

QuestioN:

• A crane on a building site lifts bricks of total mass 200kg, initially at rest on the ground, with uniform acceleration. When the bricks are 5m from the ground, they have a speed of 5m/s. How much work is done during this process?

Answer:

Correct answer is (C) 12.5 KJ.

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${\bold { \underline{\small{Explanation: }}}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\dag\:\underline{\boxed{\sf{Kinetic\: energy=\frak{\red{\bf\dfrac{1}{2}mv^2}}}}}$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\mapsto\: \bf\dfrac{1}{2} \times 2000kg \times (5m/s)^2$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 2500\:J$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= \bf\dfrac{25 \cancel{00}}{10 \cancel{00}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\normalsize{\underline{\mathcal{\green{=\:2.5\: KJ. }}}}$

$\:$

${\large{\frak{\pmb{\underline{ Now,}}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ddag\:\underline{\boxed{\sf{Potential\: energy=\frak{\red{\bf{\frak{mgh}}}}}}}$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 200 \times 10 \times 5\:m$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= 10,000 \:J$

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$\sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:= \bf\dfrac{10, \cancel{000}}{1 \cancel{000}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\normalsize{\underline{\mathcal{\purple{=\:10\: KJ. }}}}$

$\sf Work\: done = Energy \:transferred\: Kinetic\: Potential.$

$\sf\:\:\:\:\:\:\:\implies\: 10\:KJ +2.5\:KJ = \bf{\underline{12.5 \:KJ.}}$

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$\underline{\underline{\maltese \:\: \textbf{\textsf{Related\: notations}}}}$

• $\sf \:{\bf{M}} \: is\: the \:mass\: in \:kilograms.$

• $\sf \:{\bf{G}} \:is \:the\: acceleration \:due\: to\: gravity.$

• $\sf \:{\bf{H}} \: is \:the \:height\: in\:meters.$

• $\sf \:{\bf{V}}\: is\: the\: velocity\: of \:the \:body.$