Question

Two balls with masses of 1.60 kg and 5.70 kg travel toward each other at speeds of 9.0 m/s and 3.60 m/s, respectively. If the balls have a head-on inelastic collision and the 1.60-kilogram ball recoils with a speed of 7.20 m/s, how much kinetic energy is lost in the collision?

Answer 1

Given,

m1 = 1.6 kg ; m2 = 5.7 kg ; u1 = 9 m/s ; u2 = 3.6 m/s ; v1 = 7.2 m/s

Intial momentum of the system is:

Pi = m1u1 + m2u2

Pi = 1.6 x 9 + 5.7 x -3.6 = -6.12 kg-m/s

Pf = 1.6 x -7.2 + 5.7 x v2

Pf = -11.52 + 5.7 v2

from conservation of momentum

Pf = Pi

-11.52 + 5.7 v2 = -6.12

v2 = 0.95 m/s

KEi = 1/2 m1 u1^2 + 1/2 m2 u2^2

KEi = 0.5 x 1.6 x 9^2 + 0.5 x 5.7 x 3.6^2 = 101.74 J

KEf = 1/2 m1 v1^2 + 1/2 m2 v2^2

KEf = 0.5 x 1.6 x 7.2^2 + 0.5 x 5.7 x 0.95^2 = 44.04 J

KE(lost) = 44.04 - 101.74 = -57.7 J

Hence, KE(lost) = -57.7 J