Question

a girl lifts a stone weighing 10 N to a height of 2.5m how much work is done by her

Answer 1

Question:

• A girl lifts a stone weighing 10 N to a height of 2.5m how much work is done by her  

Answer:

• The work done by the girl on lifting the stone is 250 joules

Explanation:

Given:

• A girl lifts a stone weighing 10 N
• She lifts the stone to a height of 2.5 m

To Find:

• The amount of work done by her

Formula Used:

$\bigstar \; {\underline{\boxed{\bf{ Work \; done = Mgh }}}}$

Required Solution:

• Using Formula to find potential energy

★ We know that ,

${\pink{\bigstar \;{\boxed{\bf{ P. E = M_{(Mass)} \;g_{(gravitational \; acceleration)} \; h _{(height)} }}}}}$  

★ Where ,

• Mass is defined as the quantitative measure of inertia
• Height is the distance of the object raised above or dropped down
• Gravitational acceleration is the acceleration which is caused due to the gravitational force which is present on the earth

${\red{\sf{Hint : Gravitational \; acceleration = 9.8 m/s^2 }}}$  

According to the question:

• It's been said that a girl lifts a stone to a certain height and that we should we calculating the work done , So, the work done by her would be lifting the stone which would be equal to the potential energy of it

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Derivation Of Formula:

★ As it is said that , $\bf Work \; done = F\;S \; cos( \alpha )$ So , over her the force applied by the girl would be equal to  the product of mass of the body and the acceleration due to the gravity that , means F = mg and the displacement is the height moved upward S = H . As the direction of the displacement is along the force so , the angles between them is 0 [ cos ( α ) = cos ( 0 ) ]

Proving that work done is Mgh :

$\longrightarrow \sf \footnotesize W_{(Work \; done)} = F \; S \; cos ( \alpha ) \\ \\ \\\longrightarrow \sf \footnotesize W_{(Work \; done)} = Mg \; S \; cos ( \alpha) \\ \\ \\ \longrightarrow \sf \footnotesize W_{(Work \; done)} = Mgh \; cos ( 0) \qquad \lgroup \bf cos ( 0 ) equals 1 \rgroup \\ \\ \\ \longrightarrow {\sf {\red{\underline{\underline{\footnotesize {W_{(Work \; done)} = Mgh }}}}}}$

★ Henceforth ,

• Work done is equal to Mgh

★ Here we know that ,

• Force equals 10N
• Height equals 2.5m

★ As It can be written that ,

• Force = Mg ( Mass × acceleration )

★ Henceforth ,

• Mass × acceleration of gravity = 10N

$\\ \\ {\purple{\bigstar \; {\underline{\bf{ Substituting \; the \; values \; we \; get : }}}}}$

$\longrightarrow \sf \footnotesize W_{(work \; done)}= Mgh \\ \\ \\ \longrightarrow \sf \footnotesize W_{(work \; done)}= M * g * h \\ \\ \\ \longrightarrow \sf \footnotesize W_{(work \; done)}= M * g * 2.5 \\ \\ \\ \longrightarrow \sf \footnotesize W_{(work \; done)}= 10 * 2.5 \qquad \lgroup \bf Mg = 10N \rgroup \\ \\ \\ \longrightarrow {\sf {\red{\underline{\underline{\footnotesize {W_{(Work \; done)} = 25 \; Joules }}}}}}$

Therefore:

• The work done by the girl is 25 Joules

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