Question

A cardinal (Richmondena cardinalis) of mass 3.70×10⁻² kg and a baseball of mass 0.144 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude pc of momentum to the magnitude pb of the baseball's momentum?

A man weighing 750 N and a woman weighing 500 N have the same momentum. What is the ratio of the man's kinetic energy Km to that of the woman Kw?

Answer 1

(a)

KEc = KEb

KEc = 1/2mc(Vc)²

KEb = 1/2mb(Vb)²

1/2mc(Vc)² = 1/2mb(Vb)²

cancel 1/2

mc(Vc)²/mb(Vb)² = 1

(Vc)²/(Vb)² = mb/mc

Vc/Vb = √(mb/mc)

(mc/mb)(Vc/Vb) = (mc/mb)[√(mb/mc)] = Pc/Pb

mc/mb = 3.7e-2/0.144 = 0.257

√(mb/mc) = √1/0.257 = 1.97

Pc/Pb = (0.257)(1.97) = 0.507 ANS (a)

(b)

mm = 750/g = 76.53 kg

mw = 500/g = 51.02 kg

Km = Kw

mmVm = mwVw

mm/mw = Vw/Vm

76.53/51.02 = 1.50 = Vw/Vm

KEm = 1/2 mm(Vm)²

KEw = 1/2 mw(Vw)²

Km/Kw = KEm/KEw = mm(Vm)²/mw(Vw)² = mm/mw x (Vm/Vw)²

Km/Kw = 1.50 x (1/1.50)² = 1.50 x 0.444 = 0.667 ANS (b)