Question

# Consider a 20-g bullet (B) and a 60-kg runner (R). (a) If they have the same...

Consider a 20-g bullet (B) and a 60-kg runner (R). (a) If they have the same momentum, what is the ratio of their kinetic energies, KB/KR?(b) Ifthey have the same kinetic energy, what is the ratio of their momenta, PB/PR

Solution) mB = 20 g = 0.02 kg

mR = 60 kg

(a) if they have same momentum , KB/KR = ?

We have Kinetic energy , K = (1/2)(m)(v^2)

On multiplying and dividing by m

K = (1/2)(m)(v^2)(m/m)

K = (1/2)(m^2)(v^2)/(m)

Momentum P = mv

K = (1/2)((mv)^2)/(m)

K = (1/2)(P^2)/(m)

K = (P^2)/(2m)

Same momentum for bullet and Runner implies

PB = PR

So K is inversely proportional to m

(KB)/(KR) = (mR)/(mB) = (60)/(0.02) = 3000

(KB)/(KR) = 3000

(b) if they have same kinetic energy , PB/PR = ?

K = (P^2)/(2m)

KB = KR

(P^2) is proportional to m

(PB/PR)^2 = (mB/mR)

(PB/PR)^2 = (0.02/60) = 0.000333

(PB/PR) = (0.000333)^(1/2) = 0.01825

(PB/PR) = 0.01825

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