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Proveimpulse momentum equation |
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Answer» Solution :If aforce `(F )` actson a bodyin a veryshortintervalof time `(Detla t)`then formNewton'ssecondlaw inmagnitudeforms Intergratingover timeforman intialtime`t_(i)` toa finaltime `t_(f)` we get overset(i)UNDERSET(f ) (int) dp=overset(i)underset(f ) (int) Fdtg` `P_(i)- P_(i)= underset(t) overset(t)(int)F dt` `p_(1)=`initialmomentum of the bodyat time `t_(i)` `p_(f)=` finalmomentum of the bodyat time `f_(f)` `p_(f)- p_(i) = Delta p`changein MOMENTUM of thebodyduringthe TIMEINTERVAL Theintegral`underset(t ) overset( t ) (int)F dt = J` iscalledthe impulseand itis equalto change a in momentum of the body . If theforce is constantover the timeintervalthen `underset(t ) overset(t ) (int ) Fdt= Funderset( t) overset( t) dt = F (t_(1) - t_(1)) = F Delta t` `F Delta t= Delta p` Impulse = Changein momentum |
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