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
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
v2 = 5 m/s
