Two balls with the same kinetic energy have mass of ball a = m and ball b = 2m. What is the ratio of their momentums: a/b?

We know that both balls have the same kinetic energy, so we can write Eka = Ekb We also know that kinetic energy is given by the equation Ek = 1/2 (mv2) and momentum, p, is p = mv where m is the mass and v is the velocity. Since m is constant, we need an expression for the velocity of ball a, va, in terms of the velocity of ball b, vb. so the kinetic energy for ball a and b respectively is Eka = 1/2 * m * va2    Ekb = 1/2 * 2m * vb2 = m * vb2 as we know, these are equal and so 1/2 * m * va2 = m * vb2 simplifying and rearranging to find an expression for va in terms of vb we get va2 = 2 * vb2 ,  va = 21/2 vb substituting this into the equation for momentum and finding the ratio of a to b, we get p/ pb = m * 21/2vb / 2m * vb      = 21/2 / 2      = 1 / 21/2

ZR
Answered by Zachary R. Physics tutor

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