Question

body of mass 10kg initially moving with velocity 5m/s changes its velocity to 25m/s in 4 s. Calculate the
change in momentum and hence force applied

Answer 1

$\huge \underline{\fbox{Answer}}$

$\large \underline{\underline{ \frak {\color{red}Given::}}}$

$\rightarrow \sf{Mass \: of \: body(m)=10kg}$

${ \rightarrow \sf{Initial \: velocity (u) \: of \: body=5m {s}^{ - 1} }}$

${ \rightarrow \sf{ Final \: velocity (v) \: of \: body=25m {s}^{ - 1} }}$

$\sf \rightarrow{Time \: taken \: to \: change \: in \: velocity=4sec}$

$\large \underline{\underline{ \frak {\color{peru}To \: find::}}}$

$\sf \leadsto{Change \: in \: momentum \: of \: body.}$

$\sf \leadsto{Force \: required \: to \: change \: in \: velocity.}$

$\large \underline{\underline{ \frak { \pink{Formula \: required::}}}}$

$✽{ \fbox{Momentum of body(P)=mass(m)×velocity(v)}}✽$

$✽{ \boxed {\rm{Change \: in \: momentum (P) \: of \: body=Final \: momentum(P_2) \: of \: body-Initial \: momentum(P_1) \: of \: body}}}✽$

$✽{ \fbox{Force(F)=mass(m)×acceleration(a)}}✽$

$✽{ \boxed {\rm{Acceleration (a)= \frac{Change \: in \: velocity}{Time \: taken \: to \: change \: in \: velocity} }}}✽$

$\large \underline{\underline{ \frak {\color{indigo}According \: to \: Question::}}}$

${ \implies{ \sf{Initial \: momentum \: of \: body(P_1)=mass(m) \: of \: the \: body×initial \: velocity(u) \: of \: the \: body}}}$

${ \implies{ \sf{Initial \: momentum \: of \: body(P_1)=10kg \times 5m {s}^{ - 1} }}}$

${ \implies{ \sf{Initial \: momentum \: of \: body(P_1)=50kg • m {s}^{ - 1} }}}$

${ \implies{ \sf{Final \: momentum \: of \: body(P_2)=mass(m) \: of \: the \: body×final \: velocity(v) \: of \: the \: body}}}$

${ \implies{ \sf{Final \: momentum \: of \: body(P_2)=10kg \times 25m {s}^{ - 1} }}}$

${ \implies{ \sf{Final \: momentum \: of \: body(P_2)=250kg • m {s}^{ - 1} }}}$

${ \implies{ {\sf{Change \: in \: momentum (P) \: of \: body=Final \: momentum(P_2) \: of \: body-Initial \: momentum(P_1) \: of \: body}}}}$

${ \implies{ {\sf{Change \: in \: momentum (P) \: of \: body=250kg•m {s}^{ - 1} - 50kg•m {s}^{ - 1} }}}}$

${ \implies{ {\sf{Change \: in \: momentum (P) \: of \: body=200kg•m {s}^{ - 1} }}}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=mass(m)×acceleration(a)}}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=mass(m)× \frac{Final \: velocity(v)-Initial \: velocity(u)}{Time \: taken \: to \: change \: in \: velocity} }}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=10kg× \frac{25m {s}^{ - 1} -5m {s}^{ - 1} }{4sec} }}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=10kg× \frac{20m {s}^{ - 1} }{4sec}}}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=10kg×{ \cancel {\frac{20m {s}^{ - 1} }{4sec}}}}}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=10kg×{ {5m {s}^{ - 2} }}}}}$

${ \sf{ \implies{Force(F) \: applied \: on \: body=50kg•{ {m {s}^{ - 2} }}}}}$

$\large \underline{\underline{ \frak {\color{blue}Hence,}}}$

$☆{ \boxed{ {\rm{Change \: in \: momentum (P) \: of \: body=200kg•m {s}^{ - 1} }}}}☆$

$☆ \boxed{ \rm{{Force(F) \: applied \: on \: body=50N \: or \: 50kg•{ {m {s}^{ - 2} }}}}}☆$

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