Question

a force of 10N acts for 20 second on a body of mass 20kg initially at rest. calculate energy required by the body and the work done​

Answer 1

GiveN :

• Force (F) = 10N
• Time (t) = 20s
• Mass (m) = 20kg
• Initial Velocity (u) = 0 m/s

To FinD :

• Energy Required by body, and workdone

SolutioN :

Using Formula for force,

$\large{\boxed{\sf{F\ =\ ma}}} \\\\\\ \implies \sf{10\ =\ 20a} \\\\\\ \implies \sf{a\ =\ \dfrac{10}{20}} \\\\\\ \implies \sf{a\ =\ 0.5\ ms^{-2}}$

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Use 1st equation of motion

$\large{\boxed{\sf{v\ =\ u\ +\ at}}} \\\\\\ \implies \sf{ v\ =\ 0\ +\ 0.5\ \times\ 20} \\\\\\ \implies \sf{v\ = 10\ ms^{-1}}$

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Use 3rd equation of motion,

$\large{\boxed{\sf{v^2\ -\ u^2\ =\ 2as}}} \\\\\\ \implies \sf{100 = 2(0.5)(s)} \\\\\\ \implies \sf{ s\ =\ 100\ m}$

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Workdone,

$\implies \sf{W\ =\ F.s} \\\\\\ \implies \sf{ W\ =\ 10\ \times\ 100} \\\\\\ \implies \sf{W\ =\ 1000\ J}$

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Energy,

$\implies \sf{K\ =\ \dfrac{1}{2} mv^2} \\\\\\ \implies \sf{K\ =\ \dfrac{1}{2}\ \times\ 20\ \times\ 100} \\\\\\ \implies \sf{K\ =\ \dfrac{1}{2}\ \times\ 2000} \\\\\\ \implies \sf{K\ =\ 1000\ J}$