What happened to momentum if kinetic energy increase 3time?

2 Answers
Kalit Gautam
Feb 21, 2018

Momentum becomes #(3)^(1/2)# times the initial momentum given that the Mass of the object is constant.

Explanation:

#KE_i = (1/2).m.v^2# and #vecP_i = mvecv#

#KE_f = 3KE_i = 3(1/2).m.v^2 #

#rArr KE_f = (1/2).m.(v')^2# where #v' = (3)^(1/2)v#

#rArrvecP_f = mvecv' = m(3)^(1/2)vecv = (3)^(1/2)mvecv#

#:. vecP_f = (3)^(1/2)vecP_i#

Daniel H.
Feb 21, 2018

#KE=1/2mv^2# and #P=m\Deltav#

Explanation:

So, if the kinetic energy increases 3 times (triples) that means that the velocity must have increased by #sqrt3#

If you start with mass m and velocity v , as noted above #KE=1/2mv^2#

So, if the velocity increased by a factor of #sqrt3#, the new velocity is #sqrt3v# and the new kinetic energy is #KE=1/2m(sqrt3v)^2#
which is #KE=1/2m*3*v^2->3KE=1/2mv^2#

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