Question

Two objects of masses 1kg and 2 kg are moving along the same line and direction with velocities of 2 m/s and 1 m/s, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s.Find second object velocity​

Answer 1

Hello mate,

Given data in the question, M1 = The mass of first object = 1kg and M2 = The mass of second object = 2kg.

V1 = Velocity of first object before collision = 2m/s¹ and V2 = Velocity of second object before collision = 1m/s¹.

According To Question, The both objects collide and after collision, The velocity of first object after collision V3 = 1.67m/s¹. Let the velocity of second object after collision = v.

The required process to solve it:

• Momentum before collision = Momentum after collision ( It's the principle of momentum of forces that in collision the net force remains same of both velocity of respective objects only changes the just their capacity of moving ).
• 1kg × 2m/s¹ + 2kg × 1m/s¹ = 1kg × 1.67m/s¹ + 2kg × v m/s¹.
• 1 ( 2 - 1.67 ) + 2 = 2v
• 1 × 0.33 + 2 = 2v
• 0.33 + 2 = 2v
• 2v = 2.33
• v = 2.33 ÷ 2 = 1.165m/s¹.

So, The required velocity of second object after the collision 'v' is: 1.165m/s¹. ( Ans )

Note a point, in the above steps, in the 3rd step - Multiply the momentum of 1st object of before collision with the momentum of 2nd object after collision. ( and let the v of second object velocity of after collision be in the R.H.S side only and same with the second object of before collision in the L.H.S side only. )

Answer 2

Given: m₁ = 1kg, m₂ = 2kg

           u₁ = 2m/s, u₂ = 1m/s

           v₁ = 1.67 m/s

To find: The final velocity of the second object.

Solution:

• As, states in the question, this collision is an elastic collision, and this means that the law of conservation of momentum, and the law of conservation of energy will be applicable.

• The law of conservation of momentum states that in an isolated system the total momentum of two or more bodies acting upon each other remains constant unless an external force is applied.

Therefore, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where m₁ and m₂ is the mass of the first and second object respectively.

u₁ and u₂ are the initial velocities of first and second objects respectively.

v₁ and v₂ are the final velocities of first and second objects respectively.

1(2) + 2(1) = 1(1.67) + 2v₂

4 = 1.67 + 2v₂

v₂ = (4 - 1.67)/2

 = 1.165 m/s

Therefore, the velocity of the second object after the collision is 1.165 m/s