An object has a kinetic energy of 500 J due to its linear motion. What would be the kinetic energy of an object with half the mass and twice the momentum?

1 Answer
RChatterz
May 16, 2018

4000J

Explanation:

kinetic energy, #KE =1/2 mv^2# & momentum, #p=mv#
we can rewrite KE in terms of p , substituting #v=p/m#
#KE = 1/2 m (p/m)^2#
-> # KE = p^2/(2m)# let KE, m, p be for the original object and KE', m', p' for the new object
#KE' =(p')^2/(2m') # but we know from question
#m'=1/2m# & #p' = 2p#
-> #KE' = (2p)^2/(2*1/2m)#
-> #KE' = 8 * p^2/(2m)#
-> #KE' = 8*KE #
we are given #KE = 500 J# so #KE' =4000J # the final answer

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