Linear momentum calculation 1 (Collisions)

The principle of conservation of momentum:

Total momentum before collision = Total momentum after collision


Inelastic collision 

1. An object of mass = 2 kg with initial velocity of  30 m/s hit a stationary object of mass = 4 kg. After the collision, both objects move together with identical velocity. Calculate the final velocity of both objects.

Total momentum before collision 

= m₁u₁ + m₂u₂

_{= 2(30) + 4 (0)}

= 60 kg ms^-1

Total momentum after collision = 60 kg ms^-1

= m₁v₁ + m₂v₂

= 2v + 4v

= 6v

Remember

60 kg ms^-1 = 6 v

Final velocity for both objects, v = 10 ms^-1 

Elastic collision 

1. An object of mass (object 1) = 2 kg with initial velocity of  40 m/s hit an object of mass (object 2) =3 kg with initial velocity = 20 m/s. After the collision, object 1 moves with v₁ = 30 m/s. Calculate the final velocity for object 2.

Total momentum before collision

= m₁u₁ + m₂u₂

= 2 x 40 + 4 x 20

= 160 kg ms^-1

Total momentum after collision

= m₁v₁ + m₂v₂

= 2 x 30 + 4 v₂

= 60 + 4 v₂

Final velocity of object 2

160 = 60 + 4 v₂

4 v₂ = 100

v₂ = 25 ms^-1

3. Object 1 (m₁ = 2 kg) moves with  initial velocity (u₁= 20 m/s) and hits object 2 (m2 = 1 kg) (u2 = - 5 m/s) which moves in the opposite direction. After the collision, Object 1 moves with velocity = 15 m/s. Calculate the velocity for object 2, assuming that the collision is elastic.

Total momentum before collision

= 2 x 20 + 1 x (-5) negative denotes opposite direction

= 35 kg ms^-1

Total momentum after collision

= 2 x 15 + 1 x v₂

= 30 + v₂

Final velocity of object 2, moving in the same direction

35 = 30 + v₂

v_{2 =}  5 m/s