Question

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s.
After the collision, the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy
was lost during the collision?

Answer 1

Momentum = mass x velocity

Before collision
Momentum 1 = 2 kg x 20 m /s = 40 kg x m/s
Momentum 2 = 3 kg x -10m/s = -30 kg x m/s

After collision
Momentum 1 = 2 kg x -5 m/s = -10 m/s
Momentum 2 = 3 kg x V2 = 3V2

Total momentum before = total momentum after
40 + -30 = -10 + 3V2
V2 = 6.67 m/s

Total kinetic energy before
= (1/2) [ 2 kg * 20 m/s * 2 + 3 kg * ( -10 m/s) *2 ]
= 550 J

Total kinetic energy after
= (1/2) [ 2 kg * ( - 5 m/s) * 2 + 3 kg * 6.67 m/s *2 ]
= 91.73 J

Total kinetic energy lost during collision
=550 J - 91.73 J
= 458.27 J

Answer 2

Kinetic energy before:

E = 0.5mv^2 + 0.5mv^2

= 0.5*2*20^2 + 0.5*3*(-10)^2

= 400 + 150

= 550J

Kinetic energy after:

E = 0.5mv^2

= 0.5*2*(-5)^2

= 25J

Kinetic energy lost during the collision:

E = 550 - 25

= 525J