Chpter 6 physics homework

Question

1)A cardinal of mass 3.50×10−2 kg and a baseball of mass 0.142 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude p_c of momentum to the magnitude p_b of the baseball's momentum?

2) A man weighing 720 N and a woman weighing 500 N have the same momentum. What is the ratio of the man's kinetic energy K_m to that of the woman K_w?

Answer 1

For problem (1), K = (1/2) m v²  =  p² / (2 m).

If two things have the same kinetic energy, then that means that:

(p1)² / (2 m1) = (p2)² / (2 m2).

(p1/p2)²  = m1/m2.

p1/p2 = sqrt(m1 / m2).

For problem (2), if p1 = p2 = p, then K1 = p² / (2 m1), and K2 =  p² / (2 m2).

That means that 2 m1 K1 = 2 m2 K2, which means that K1/K2 = m2 / m1.

Do you see the general strategy here? Because if you don't, then plugging in the numbers won't help you on the eventual test. The strategy is to just *write down what you know* and then *play with the math* until it's in the form you want.