Question

calculate the work done required to stop a car of mass 50 kg moving witha velocity of 54 km/h



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Answer 1

Answer:

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}✠Given:−</p><p>\begin{gathered}\sf\implies Mass \ of \ the \ car \ is \ 50kg .\\\sf\implies Initial\ Velocity \ is \ 54km/h. \end{gathered}⟹Mass of the car is 50kg.⟹Initial Velocity is 54km/h.</p><p>\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}✠To Find:−</p><p>\sf\implies The \ work \ done \ to \ stop \ the \ car .⟹The work done to stop the car.</p><p>\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}✠Answer:−</p><p>We will use Work Energy Theorem to find the work done , according to which work done is equal to the change in the Kinetic energy i.e. ∆ K.E. Since the car will be stopped the final Velocity will be 0m/s.</p><p>\underline{\purple{\boldsymbol{ According \ to \ Work \ Energy \ Theorem :- }}}According to Work Energy Theorem:−</p><p>\begin{gathered}\sf:\implies\pink{ Work \ Done = \Delta Energy_{Kinetic\ energy } }\\\\\sf:\implies Work \ Done = \dfrac{1}{2}mv^2- \dfrac{1}{2}mu^2 \\\\\sf:\implies Work \ Done = \dfrac{1}{2}m ( v^2 - u^2 ) \\\\\sf:\implies Work \ Done = \dfrac{1}{2}\times 50kg [ (0m/s)^2 - (54km/hr)^2 ] \\\\\sf:\implies Work \ Done = 25kg \bigg\lgroup 0m^2/s^2 - \bigg(54 \times \dfrac{5}{18}m/s.\bigg)^2 \bigg\rgroup \\\\\sf:\implies Work \ Done = 25kg [ 0m^2/s^2 - (15m/s)^2 ] \\\\\sf:\implies Work \ Done = 25kg \times - 225 m^2/s^2 \\\\\mathfrak:\implies \boxed{\pink{\mathfrak {Work \ Done = -5625 \ Joules .} }}\end{gathered}:⟹Work Done=ΔEnergyKinetic energy:⟹Work Done=21mv2−21mu2:⟹Work Done=21m(v2−u2):⟹Work Done=21×50kg[(0m/s)2−(54km/hr)2]:⟹Work Done=25kg⎩⎪⎪⎪⎧0m2/s2−(54×185m/s.)2⎭⎪⎪⎪⎫:⟹Work Done=25kg[0m2/s2−(15m/s)2]:⟹Work Done=25kg×−225m2/s2:⟹Work Done=−5625 Joules.</p><p>\underline{\blue{\sf \therefore Hence \ the \ work \ done \ is \ \textsf{\textbf{-5625 \ Joules }}. }}∴Hence the work done is -5625  Joules .</p><p>$

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Answer 2

work done = /\ E = Net energy

= 1/2 mv^2 - 1/2mu^2

= 0 - 1/2×50×(54×5/18)^2

= -5625 Joules..

Hope it helps you...