Question

find out the work done by a machine in lifting a mass of 40kg to a hight of 10m​

Answer 1

Answer : 3920j = 3.92kJ

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$\begin{gathered}\begin{gathered}\pink{ \frak{Given}} \begin{cases} \sf \: </strong><strong>Mass</strong><strong> \</strong><strong> </strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>4</strong><strong>0</strong><strong>k</strong><strong>g</strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong> </strong><strong>Height</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>0</strong><strong>m</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>Gravity</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>9</strong><strong>.</strong><strong>8</strong><strong>m</strong><strong>/</strong><strong>s²</strong><strong> </strong><strong>\end{cases} \\ \\\end{gathered}\end{gathered}$

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SOLUTION:

Work done can be calculated by using this formula

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:</strong><strong> </strong><strong>W </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>F.a</strong><strong> </strong><strong>=</strong><strong> </strong><strong>mgh</strong><strong> }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \: </strong><strong>W </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>4</strong><strong>0</strong><strong>k</strong><strong>g</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>×</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>9</strong><strong>.</strong><strong>8</strong><strong>m</strong><strong>/</strong><strong>s²</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>×</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>0</strong><strong> \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: W \: = \: </strong><strong>3</strong><strong>9</strong><strong>2</strong><strong>0</strong><strong>j</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>3</strong><strong>.</strong><strong>9</strong><strong>2</strong><strong>k</strong><strong>J</strong><strong> }} }\\ \\\end{gathered}\end{gathered}$

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Answer 2

Given:

Mass of body = 40kg

Height raised = 10m

Solution:

We know that,

F= ma

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Taking the value of g as 9.8m/s²

$\sf{\implies}{F= 40 \times 9.8}$

$\sf{\implies}{F= 392N}$

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Also, $\sf{Work \:Done = Force \times Displacement}$

$\sf{\therefore W= 392 \times 10}$

$\sf{W=3920 J}$

or, Work done = 3.92 KJ