How to find momentum when kinetic energy increase or decrease?

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Answer 1 · 2018-04-24T13:53:19

#"p"_f = "p"_i × sqrt("K"_f/"K"_i)#

Kinetic energy is given by

#"K" = 1/2\ "mv"^2#

Momentum (#"p"#) is given by

#"p = mv"#

On combing both the formulas we get

#"K" = "p"^2/"2m"#

So, for an object of mass #"m"#

#"p" ∝ sqrt"K"#

#"p"_i/"p"_f = sqrt("K"_i/"K"_f)#

#color(blue)("p"_f = "p"_i × sqrt("K"_f/"K"_i))#

Example: Kimetic energy is increased by #21%# what is percentage increase in momentum?

Solution: #"p"_f = 100% × sqrt((100% + 21%)/(100%)) = 110%#

Increase in momentum#= "p"_f - "p"_i = 110% - 100% = 10%#