(a) Show that the kinetic energy ?K? and the momentum magnitude ?p? of a particle with mass m are related by ?K? = ?p?2/2?m?. (b) A 0.040-kg cardinal (?Richmondera cardinalis?) and a 0.145-kg baseball have the same kinetic energy. Which has the greater magnitude of momentum? What is the ratio of the cardinal’s magnitude of momentum to the baseball’s? (c) A 700-N man and a 450-N woman have the same momentum. Who has the greater kinetic energy? What is the ratio of the man’s kinetic energy to that of the woman?

Solution 3E Step 1 of 3: a) he momentum is the product of mass and velocity p = mv v = p m The kinetic energy is, K.E = mv 2 2 1 p 2 Then K.E = m(2) m 2 = p 2m Step 2 of 3: b) (K.E) = (K.E) C B p2 p2 C = B 2mC 2mB m pB= Bpc mC = 0.145 pg 0.040 kgC p = 1.9 p B c The base ball has the greater magnitude of momentum p pC = 1.9 B = 0.526