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
May 16, 2018

4000J

Explanation:

kinetic energy, KE =1/2 mv^2KE=12mv2 & momentum, p=mvp=mv
we can rewrite KE in terms of p , substituting v=p/mv=pm
KE = 1/2 m (p/m)^2KE=12m(pm)2
-> KE = p^2/(2m)KE=p22m 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