Question #6a327

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Answer 1 · 2017-10-21T01:13:20

Doubles.

Kinetic energy can be written in terms of momentum:

#K=1/2mv^2#

#=>=(mv)^2/(2m)#

#=>color(blue)(K=p^2/(2m))#

We can then rearrange to write momentum in terms of the kinetic energy:

#=>p^2=K*2m#

#=>color(blue)(p=sqrt(2Km))#

If the kinetic energy increases by a factor of 4, we have now that #K=4K#.

#=>p=sqrt(2*4K*m)#

#=>color(blue)(p=2sqrt(2Km))#

#:.# The momentum doubles.