Question

If two objects of mass 20kg and 40kg moving towards eacho ther with same speed 20m/s, and after collision they both stick together then find speed of both after collision

Answer 1

Given :-

▪ Two objects of mass 20 kg and 40 kg moving towards each other with same speed v = 20 m/s.

▪ Both objects stick to each other after the collision.

To Find :-

▪ Speed of both after collision.

Solution :-

According to the law of conservation of momentum, the momentum of the system before and after the collision would be conserved and same.

So, Let us find the momentum of the system before collision. We can take the velocity of any of the two objects negative.

Now, we have

Object 1

• Mass, m = 20 kg
• Velocity, v = + 20 m/s

Object 2

• Mass, M = 40 kg
• Velocity, V = -20 m/s

Momentum of the system,

⇒ Momentum of Obj. 1 + Momentum of Obj. 2

⇒ mv + MV

⇒ 20 × 20 + 40 × -20

⇒ 400 - 800

⇒ -400 kg.m/s

Given that the objects stick together after the collision so it forms a object of mass of the objects. So We have

• Mass of object, M' = M + m

⇒ Mass, M' = 60 kg

• Speed, v' = x

As we have discussed before, momentum is conserved.

So,

⇒ Momentum before collision = Momentum after collision

⇒ -400 = M' v'

⇒ -400 = 60 × v'

⇒ v' = -6.67 m/s

Hence, The velocity of the combined object after collision will be 6.67 m/s in the direction of heavier object.