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We know that
so you can see the relation by computing this two.
Let us massage equation 2 a bit, for convenience:
Now we can plug this into our Kinetic energy equation, by replacing v for p/m, which yields:
which, after manipulating a little will shorten to:
And now we have a relation between K and p. Let us now see what happens when you increase p by 20%.
An increase by 20% in p can be expressed as 1.2*p . So if you replace, in the last equation, p by 1.2*p, you will end up with
So, if you increase the momentum by 20%(1.2), the Kinetic energy will increase by a factor of 1.44 or, in percentage, by 44%.
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