A railway coach of mass 10 tonnes moves with a speed of 15 m/sec & stkires the stationery coach of mass 5 tonnes . After collision the carriages move together . What is their common speed & in Wch direction will they move??
Answers
Given :
- Mass of Railway coach, m₁ = 10 Tonnes = 10 × 1000 kg = 10,000 kg
- Initial velocity of Railway coach, u₁ = 15 m/s
- Mass of second Railway coach, m₂ = 5 tonnes = 5 × 1000 kg = 5,000 kg
- Initial velocity of Second Railway coach, u₂ = 0
After the collision, the carriages move together. so
- Let, Final velocity of first Railway coach, v₁ = Final velocity of second railway coach, v₂ = v
To find :
- Common speed/velocity of two Railway coaches, let v =?
Knowledge required :
- Law of conservation of momentum
During a collision ocuring in a system of two bodies, the total momentum before collision will be equal to the total momentum after collision.
→ total Initial momentum = total final momentum
→ m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
[ Where m₁ and m₂ are masses of two bodies with Initial velocities before collision u₁ and u₂ and final velocities after collision v₁ and v₂ respectively ]
Solution :
Using the Law of conservation of momentum
→ m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
→ (10,000) (15) + (5,000) (0) = (10,000) (v) + (5,000) (v)
→ 1,50,000 = v ( 10,000 + 5,000 )
→ 1,50,000 = 15,000 . v
→ v = 1,50,000 / 15,000
→ v = 10 m/s
Therefore,
- Common speed of Railway coaches will be 10 m/s .
- And they will move in the same direction as the direction of initial velocity of first Railway coach.
Solution :
Using the Law of conservation of momentum ☄❁
→ m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
→ (10,000) (15) + (5,000) (0) = (10,000) (v) + (5,000) (v)
→ 1,50,000 = v ( 10,000 + 5,000 )
→ 1,50,000 = 15,000 . v
→ v = 1,50,000 / 15,000
→ v = 10 m/s ✔
Therefore,
➦Common speed of Railway coaches be 10 m/s .
➦And they will move in the same direction as the direction of initial velocity of first Railway coach.