Question

Two balls with masses of 2.30 kg and 5.90 kg travel toward each other at speeds of 11.0 m/s and 4.30 m/s, respectively. If the balls have a head-on inelastic collision and the 2.30-kilogram ball recoils with a speed of 8.60 m/s, how much kinetic energy is lost in the collision?

Answer 1

here,

mass of ball 1 , m1 = 2.3 kg

mass of ball2 , m2 = 5.9 kg

initial speed of ball 1 , u1 = 11 m/s

initial speed of ball 2 , u2 = - 4.3 m/s

final speed of ball 1 , v1 = - 8.6 m/s

let the final speed of ball 2 be v2

using conservation of momentum

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

2.3 * 11 - 5.9 * 4.3 = - 2.3 * 8.6 + 5.9 * v2

solving for v2

v2 = 3.34 m/s

the kinetic energy lost in the collison, KE = KEi - KEf

KE = (0.5 * m1 * u1^2 + 0.5 * m2 * u2^2) - ( 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2)

KE = 0.5 * ( (2.3 * 11^2 + 5.9 *4.3^2) - ( 2.3 * 8.6^2 + 5.9 * 3.34^2)) J

KE = 75.7 J